# Real Statistics Using Excel

> Everything you need to perform real statistical analysis using Excel

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## Posts

- [Blogs](https://real-statistics.com/blogs/)
- [Real Statistics Release 8.3](https://real-statistics.com/real-statistics-release-8-3/)
- [Real Statistics Release 7.4](https://real-statistics.com/real-statistics-release-7-4/): Describes the features of the latest Real Statistics release, including bounded linear regression and the Cochran-Armitage test.
- [Real Statistics Release 7.6](https://real-statistics.com/real-statistics-release-7-6/): Describes Release 7.6 of the Real Statistics software, Includes minimum spanning tree, network graphs and improved bivariate normal distribution support.
- [Release 4.6 Announcement](https://real-statistics.com/release-4-6-announcement/): Describes the new features in the latest release of the Real Statistics add-in.
- [Real Statistics Release 8.4](https://real-statistics.com/real-statistics-release-8-4/)
- [Release 4.5 Announcement](https://real-statistics.com/release-4-5-announcement/): Describes the latest release of the Real Statistics add-in to perform statistical analysis in Excel. Includes d'Agostino-Pearson test and Bland-Altman.
- [Real Statistics Release 4.4](https://real-statistics.com/real-statistics-release-4-4/): Describes the latest release of the Real Statistics Resource Pack, an Excel add-in for statistical analysis. Includes robust standard errors and Gage R&R.
- [Release 4.3 of Real Statistics Resource Pack](https://real-statistics.com/release-4-3-real-statistics-resource-pack/): Description of the latest release of the Real Statistics software, a free Excel add-in for statistical analysis. Focus is on survival analysis.
- [Release 4.0 of Real Statistics Resource Pack](https://real-statistics.com/release-4-real-statistics-resource-pack/): Describes the latest release of the Real Statistics Resource Pack, including cluster analysis, exponential regression, multivariate logistic regression.
- [Release 3.8 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-8-real-statistics-resource-pack/): Describes features in latest release of the free Real Statistics software, incl. nonlinear exponential regression and confidence intervals for weighted kappa.
- [Release 3.7 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-7-real-statistics-resource-pack/): Describes the new features in the Real Statistics Resource Pack for performing statistical analysis in Excel
- [Release 2.5 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-5-real-statistics-resource-pack/): Description of the latest release of the Real Statistics Resource Pack and recent changes to the website.
- [Release 1.8.2 of the Real Statistics Resource Pack](https://real-statistics.com/release-1-8-2-of-the-real-statistics-resource-pack/)
- [Real Statistics Resource Pack Rel 9.9](https://real-statistics.com/real-statistics-resource-pack-rel-9-9/): Describes the latest release of the Real Statistics statistical analysis software. The focus of this release is on Markov chain capabilities.
- [Real Statistics Release 9.8](https://real-statistics.com/real-statistics-release-9-8/): Describes the features in the latest release of the Real Statistics Resource Pack, Rel 9.8, a free statistical analysis tool for Excel environments.
- [Real Statistics Release 7.0](https://real-statistics.com/real-statistics-release-7-0/): Describes the new features of the latest release of the Real Statistics software, which expands the statistical analysis capabilities of Excel
- [Real Statistics Release 6.8](https://real-statistics.com/real-statistics-release-6-8/): Describes the new features of the latest release of the Real Statistics software, which expands the statistical analysis capabilities of Excel
- [Real Statistics Release 6.7](https://real-statistics.com/real-statistics-release-6-7/): Describes the new features in the Real Statistics Resource Pack, a free Excel add-in for statistical analysis. Includes Permutation MANOVA and trinomial test.
- [Real Statistics Release 6.6](https://real-statistics.com/real-statistics-release-6-6/): Describes the new features in the latest release of the Real Statistics software, an Excel add-in to perform statistical analysis
- [Real Statistics Release 6.5](https://real-statistics.com/real-statistics-release-6-5/): Describes the latest release of the Real Statistics Resource Pack, an Excel add-in that provides a great variety of statistical analysis capabilities
- [Real Statistics Release 6.4](https://real-statistics.com/real-statistics-release-6-4/)
- [Real Statistics Release 5.11](https://real-statistics.com/real-statistics-release-5-11/): Describes the features in the latest release of the Real Statistics free statistical analysis add-in to Excel 2007 and 2011
- [Real Statistics Release 6.2](https://real-statistics.com/real-statistics-release-6-2/): Describes the new capabilities in the Real Statistics Resource Pack, a free Excel add-in for statistical analysis
- [Real Statistics Release 6.3](https://real-statistics.com/real-statistics-release-6-3/): Describes new features and bug fixes in Real Statistics Release 6.3.
- [Real Statistics Release 6.1](https://real-statistics.com/real-statistics-release-6-1/): Describes the features in the latest release of the Real Statistics free statistical analysis add-in to Excel.
- [Real Statistics Release 5.4](https://real-statistics.com/real-statistics-release-5-4/)
- [Real Statistics Release 9.7.6](https://real-statistics.com/real-statistics-release-9-7-6/): Announces Real Statistics Rel 9.7.6. This release corrects the errors that were inadvertantly included in Real Statistics Rel 9.7.5.
- [Real Statistics Release 9.7.5](https://real-statistics.com/real-statistics-release-9-7-5/): Describes the features of the latest release of the Real Statistics Resource Pack, Rel 9.7.5. This release provides some new fetaures and bug fixes.
- [Real Statistics Release 9.7](https://real-statistics.com/real-statistics-release-9-7/): Describes the new capabilities in Real Statistics Rel 9.7. Includes Partial Least Squares (PLS) Regression, Multivariate Regression, Bootstrapping in Regression
- [Real Statistics Release 8.0](https://real-statistics.com/real-statistics-release-8-0/): Describes the new features in Rel 8.0 of the Real Statistics statistical analysis add-in to Excel. Incl. panel, repeated measures ANOVA, Lambda-like features.
- [Real Statistics Release 9.6.1](https://real-statistics.com/real-statistics-release-9-6-1/): Describes the new capabilities provided in the latest release, Rel 9.6.1, of the popular, free Real Statistics statistical analysis add-in to Excel.
- [Real Statistics Release 9.6](https://real-statistics.com/real-statistics-release-9-6/): Describes the new capabilities provided in the latest release, Rel 9.6, of the popular, free Real Statistics statistical analysis add-in to Excel.
- [Real Statistics Release 9.5.5](https://real-statistics.com/real-statistics-release-9-5-5/): Describes the new features in Rel 9.5.5 of the Real Statistics statistical analysis add-in to Excel. Focus is on new Bayesian support and differential equations
- [Real Statistics Release 9.5](https://real-statistics.com/real-statistics-release-9-5/): Describes new features of Real Statistics which provides additional statistical analysis capabilities in Excel. The focus of this release is Bayesian statistic.
- [Real Statistics Rel 9.4.5](https://real-statistics.com/real-statistics-rel-9-4-5/): Describes the new features provided by the latest release of the Real Statistics free statistical analysis add-in to Excel.
- [Real Statistics Rel 9.4](https://real-statistics.com/real-statistics-rel-9-4/): Describes the features of the latest release of the Real Statistics statistical add/in to Excel. Includes propensity score matching and coarsened exact matching
- [Real Statistics Resource Pack Release 9.3](https://real-statistics.com/real-statistics-resource-pack-release-9-3/): Provides a description of the new features of Release 9.3 of the Real Statistics add-in to Excel for statistical analysis. Includes GMM.
- [Real Statistics Release 9.2.2](https://real-statistics.com/real-statistics-release-9-2-2/): Describes the new bug-fix release for the Real Statistics Resource Pack, Release 9.2.2. Only change is for Gwet's AC2 and Krippendorff's alpha.
- [Real Statistics Release 9.2.1](https://real-statistics.com/real-statistics-release-9-2-1/): Describes the new features in the latest release of the Real Statistics Resource Pack, Rel 9.2.1, as well as the various bug fixes.
- [Real Statistics Release 9.2](https://real-statistics.com/real-statistics-release-9-2/): Describes the new features in the latest release, Rel 9.2, of the Real Statistics statistical analysis add-in to Excel. Includes Tobit regression.
- [Real Statistics Release 9.1.1](https://real-statistics.com/real-statistics-release-9-1-1/): Describes the bugs that have been fixed in the latest release of the Real Statistics statistical add-in to Excel. Also includes a new lambda feature.
- [Real Statistics Release 9.1](https://real-statistics.com/real-statistics-release-9-1/): Describes the features in the latest release of the Real Statistics statistical add-in to Excel, Release 9.1. Includes Brunner-Munzel test and Taguchi DOE.
- [Real Statistics Rel 9.0 for Mac](https://real-statistics.com/real-statistics-rel-9-0-for-mac/): Announcing Release 9.0 of the Real Statistics Resource Pack for Mac users. See the previous blog for a complete description of the release.
- [Real Statistics Release 9.0](https://real-statistics.com/real-statistics-release-9-0/): Describes the new features in the latest release of the Real Statistics Resource Pack, namely Rel 9.0. This release adds Neural Network support
- [Real Statistics Release 8.1.5](https://real-statistics.com/real-statistics-release-8-1-5/): Describes the new features provided by the latest release of the Real Statistics Resource Pack, software that augments Excel's statistical analysis capabilities
- [Real Statistics Release 8.2](https://real-statistics.com/real-statistics-release-8-2/): Describes the new features in Rel 8.2 of the Real Statistics Resource Pack. These calculate a winning strategy for Wordle and enhance the Anderson-Darling test.
- [How to win at Wordle](https://real-statistics.com/how-to-win-at-wordle/): Describes a strategy for how to choose your guesses to maximize your chances of finding Wordle's target word in at most 3 guesses. Includes Excel support.
- [Real Statistics Release 8.3.1](https://real-statistics.com/real-statistics-release-8-3-1/): Announces the latest bug-fix release of the Real Statistics Resource Pack, Rel 8.3.1,an Excel add-in for statistical analysis.
- [Update for Mac Users](https://real-statistics.com/update-for-mac-users/): Describes upcoming new support for Mac users.
- [Real Statistics Release 5.7](https://real-statistics.com/release-5-7/): Describes the new features in the latest release of the Real Statistics software, which provides a robust range of statistical analysis capabilities in Excel.
- [Real Statistics Release 5.6](https://real-statistics.com/real-statistics-release-5-6/): Describes the new features in the Real Statistics Resource Pack Release 5.6, including support for analyses where there is missing data using the EM algorithm, Dot Plots and Cochrane-Orcutt regression.
- [Real Statistics Release 5.1](https://real-statistics.com/real-statistics-release-5-1/): Describes the new features in Release 5.1 of the Real Statistics Resource Pack, a free statistical analysis addin for Excel.
- [Release 5.0](https://real-statistics.com/release-5-0/): Describes the new features in Release 5.0 of the Real Statistics Resource Pack.
- [Real Statistics Release 7.3](https://real-statistics.com/real-statistics-release-7-3/): Describes the features in the latest Real Statistics software release. Incl. simulated exact chi-square test, Rasch polytomous analysis, MSSD, Kronecker product
- [Real Statistics Release 7.1](https://real-statistics.com/real-statistics-release-7-1/): Describes the new features & bug-fixes in the latest Real Statistics release. Real Statistics is a software package that performs statistical analysis in Excel
- [Real Statistics Release 7.2](https://real-statistics.com/real-statistics-release-7-2/): Describes the new features in the latest release of the Real Statistics software package which provides statistical analysis capabilities in Excel.
- [Real Statistics Release 5.9](https://real-statistics.com/real-statistics-release-5-9/)
- [Real Statistics Rel 4.12](https://real-statistics.com/real-statistics-rel-4-12/): Describes the new features in Release 4.12 of the Real Statistics Resource Pack, a popular Excel addin for doing statistical analysis.
- [Real Statistics Release 5.3](https://real-statistics.com/real-statistics-release-5-3/): Describes the features in the latest release of the Real Statistics Resource Pack, including Ridge regression and LASSO regression
- [Real Statistics Release 5.8](https://real-statistics.com/real-statistics-release-5-8/): Describes the new features of Release 5.8 of the Real Statistics Resource Pack, an Excel addin that provides a variety of statistical analysis capabilities
- [Real Statistics Release 6.0](https://real-statistics.com/real-statistics-release-6/): Describes the features in the latest release, Rel 6.0, of the Real Statistics statistical analysis software. This is free software that works in Excel.
- [Release 5.0 for Mac](https://real-statistics.com/release-5-0-for-mac/): Describes the latest release (5.0) of the Real Statistics Resource Pack for Mac computers
- [Changes to Website](https://real-statistics.com/changes-to-website/): New theme for Real Statistics. Seeking comments and suggestions.|
- [Real Statistics Release 7.5](https://real-statistics.com/real-statistics-release-7-5/): Describes the latest release of the Real Statistics statistical analysis software for Excel users. Focus is eigenvalues/vectors and Lp-based cluster analysis
- [Real Statistics Release 7.7](https://real-statistics.com/real-statistics-release-7-7/): Describes Release 7.7 of the Real Statistics software, Includes ordinal regression, improved binary logistic and Probit regression and a new version of ANCOVA.
- [Real Statistics Release 7.8](https://real-statistics.com/real-statistics-release-7-8/): Describes the new capabilities and bug fixes in the latest release of the Real Statistics Resource Pack that enhances statistical analysis support in Excel.
- [Real Statistics Release 7.9](https://real-statistics.com/real-statistics-release-7-9/): Describes the new features in the latest release of the Real Statistics Resource Pack, Rel 7.9, an Excel-based platform for statistical analysis,
- [Real Statistics Release 7.10](https://real-statistics.com/real-statistics-release-7-10/): Describes the new capabilities (rooting finding, GEV distribution, etc.) provided in the latest release, Rel 7.10, of the Real Statistics Resource Pack.
- [Real Statistics Release 8.1](https://real-statistics.com/real-statistics-release-8-1/): Describes the new features in the latest release, Rel 8.1, of the free Real Statistics statistical software package, designed to work with Excel.
- [Real Statistics Release 8.8](https://real-statistics.com/real-statistics-release-8-8/): Describes the new features in the latest release of the Real Statistics Resource Pack, an Excel add-in for statistical analysis
- [Real Statistics Release 8.7](https://real-statistics.com/real-statistics-release-8-7/): Describes the new features in the latest release of the Real Statistics Resource Pack, an Excel add-in for statistical analysis
- [Real Statistics Release 8.9](https://real-statistics.com/real-statistics-release-8-9/): Describes the new capabilities in the latest release, Rel 8.9, of the Real Statistics Resource Pack, an Excel add-in for statistical analysis
- [Real Statistics Release 8.8.1](https://real-statistics.com/real-statistics-release-8-8-1/): Describes the new features in the latest release of the Real Statistics Resource Pack, Rel 8.8.1, as well as the latest bug fixes.
- [Real Statistics Release 8.8.2](https://real-statistics.com/real-statistics-release-8-8-2/): Describes the new features of the latest release of the Real Statistics software, Release 8.8.2. This release contains bug fixes and O'Brien's test support.
- [Real Statistics Release 8.5](https://real-statistics.com/real-statistics-release-8-5/): Describes the new features in Rel 8.5 of the Real Statistics Resource Pack, an Excel add-in that enhances the statistical analysis capabilities of Excel
- [Real Statistics Release 8.6.3](https://real-statistics.com/real-statistics-release-8-6-3/): Describes the latest bug fix release of the Real Statistics Resource Pack, an add-in to Excel that performs enhanced statistical analyses.
- [Real Statistics Release 8.6](https://real-statistics.com/real-statistics-release-8-6/): Describes the new features in Rel 8. of the Real Statistics Resource Pack, an Excel add-in that enhances the statistical analysis capabilities of Excel
- [Real Statistics Release 8.6.1](https://real-statistics.com/real-statistics-release-8-6-1/): Describes the latest bug-fix release of the Real Statistics Resource Pack, Rel 8.6., a free statistical analysis add-in to Excel.
- [Real Statistics Release 8.9.1](https://real-statistics.com/real-statistics-release-8-9-1/): Describes the bug fixes and new capabilities in the latest release, Rel 8.9.1, of the Real Statistics Resource Pack, an Excel add-in for statistical analysis.
- [Release 8.2.1](https://real-statistics.com/release-8-2-1/): Describes the latest release, Rel 8.2.1, of the Real Statistics Resource Pack, an Excel add-in that supports a variety of statistical analysis capabilities.
- [Real Statistics Release 8.1.6](https://real-statistics.com/real-statistics-release-8-1-6/): Describes the bug fixes in Release 8.1.6 of the Real Statistics Resource Pack, which is an Excel add-in providing advanced statistical analysis capabilities.
- [Note about Rel 8.0](https://real-statistics.com/note-about-rel-8-0/)
- [Note about Rel 7.10](https://real-statistics.com/note-about-rel-7-10/): Update about the status of Real Statistics Rel 7.10. Also, includes a correction about support for the Harrell-Davis version of the MAD.
- [Real Statistics Release 7.7.2](https://real-statistics.com/real-statistics-release-7-7-2/): Describes the features in the latest bu-release version of the Real Statistics Resource Pack. This release also includes a few new functions.
- [Release 7.6.1](https://real-statistics.com/release-7-6-1/): Real Statistics Rel 7.6.1 is a bug-fix release. Includes fixes to Two-Factor MANOVA, HC4 errors for Robust Regression and distance values for Friedman-Rafsky.
- [Release 7.3.3](https://real-statistics.com/release-7-3-3/)
- [Real Statistics Release 7.0.5](https://real-statistics.com/real-statistics-release-7-0-5/)
- [Real Statistics Release 7.0.2](https://real-statistics.com/release-7-0-2/): Describes the latest bug-fix release
- [Real Statistics Release 7.0.1](https://real-statistics.com/real-statistics-release-7-0-1/): Bug-fix release. Fixes a bug in a sort routine used by a number of Real Statistics functions. Also, fixes a bug in the Regression data analysis tool for Mac.
- [Real Statistics Release 6.6.2](https://real-statistics.com/real-statistics-release-6-6-2/): Describes the changes introduced in Rel 6.6.2 of the Real Statistics Resource Pack.
- [Problems introduced by latest Excel 365 release](https://real-statistics.com/problems-latest-version-excel-365/)
- [Bug Fix Release 6.2.1](https://real-statistics.com/bug-fix-release-rel-6-2-1/): Announces a bug-fix release for Windows users. Not required for Mac users.
- [Bug Fix Release 6.2.2](https://real-statistics.com/bug-fix-release-6-2-2/): Fixes a bug in the COV2Pooled function
- [Real Statistics Rel 6.2 for Mac](https://real-statistics.com/real-statistics-rel-6-2-for-mac/): Announces that the latest release of the Real Statistics software is now available for Mac users
- [Compile Error in Hidden Module](https://real-statistics.com/compile-error-in-hidden-module/): Describe how to deal with the error message "Compile error in hidden module …"
- [Real Statistics Release 5.10.1](https://real-statistics.com/real-statistics-release-5-10-1/): Describes the latest Real Statistics release for Excel 2007 and Excel 2011 users.
- [Real Statistics Release 6.0.4](https://real-statistics.com/real-statistics-release-6-0-4/): Describes the changes in Real Statistics Release 6.0.4
- [Real Statistics Release 5.10](https://real-statistics.com/release-5-10/): Describes the new release of the Real Statistics Resource Pack for Excel 2007 and 2011 users. This release contains a subset of Rel 6.0.2 capabilities.
- [Bug Fix Release 6.0.2](https://real-statistics.com/bug-fix-release-6-0-2/): Fixes a bug related to the chi square distribution
- [Bug Fix Release 6.0.1](https://real-statistics.com/bug-fix-release-6-0-1/): Fixes a serious bug
- [Real Statistics Rel 5.9.2 for Mac](https://real-statistics.com/real-statistics-rel-5-9-2-mac/): This release fixes an error in the T Test and Non-parametric Equivalents data analysis tool.
- [Real Statistics Rel 5.9.1 for Mac](https://real-statistics.com/real-statistics-rel-5-9-1-for-mac/): Describes the latest release of the Real Statistics Resource Pack for the Mac.
- [Error in MWDIST Function](https://real-statistics.com/error-mwdist-function/): Reports on a bug in the MWDIST function and how to correct it
- [Release 5.7 for Mac](https://real-statistics.com/release-5-7-for-mac/): Announces new release, Release 5.7, is now available for the Mac (Excel 2011 and Excel 2016)
- [Real Statistics Release 5.5](https://real-statistics.com/real-statistics-release-5-5/): Describes all the new features in the latest release of the Real Statistics Resource Pack. Especially useful are confidence intervals for effect size and power, Jonckheere–Terpstre Test, Breusch-Godfrey Test and Newey-West
- [Release 5.4.2](https://real-statistics.com/release-5-4-2/): Describes a minor release consisting of two bug fixes.
- [Release 5.4.1](https://real-statistics.com/release-5-4-1/)
- [Release 5.3.2](https://real-statistics.com/release-5-3-2/)
- [Release 5.3.1](https://real-statistics.com/release-5-3-1/): Describes the latest release to the Real Statistics Resource Pack
- [Release 5.3 for Mac Users](https://real-statistics.com/release-5-3-for-mac-users/): Announces that Release 5.3 of the Real Statistics Resource pack is now available for Mac users of Excel 2011 and Excel 2016
- [Release 5.2](https://real-statistics.com/release-5-2/): Provides a description of the new capabilities in Release 5.2 of the Real Statistics Resource Pack, esp. including enhanced Arima features
- [More about Release 5.1](https://real-statistics.com/more-about-release-5-1/): Describes one new feature in Release 5.1, namely follow up testing after Three Factor ANOVA and provides a quick update on the release.
- [Release 4.14](https://real-statistics.com/release-4-14/): Describes the new features of the Real Statistics Resource Pack, an Excel addin for statistics analysis.
- [Release 4.13](https://real-statistics.com/release-4-13/): Describes the new features in the latest release (Rel 4.13) of the Real Statistics addin to Excel
- [Real Statistics with 64 bit Excel](https://real-statistics.com/real-statistics-with-64-bit-excel/)
- [Access via Quick Access Toolbar or Ribbon](https://real-statistics.com/quick-access-toolbar-ribbon/): Update on how to access the Real Statistics data analysis tools using the Quick Access Toolbar or via an existing Ribbon
- [Real Statistics Rel 4.11](https://real-statistics.com/real-statistics-rel-4-11/): Describes the new features in the latest release of the Real Statistics free addin for doing statistical analysis in Excel
- [Real Statistics Rel 4.10](https://real-statistics.com/23379-2/): Describes the features in the latest release of the Real Statistics Resource Pack, a free Excel addin for statistical analysis.
- [Real Statistics disappears from Addin ribbon](https://real-statistics.com/real-statistics-disappears-from-addin-ribbon/): Describes how to solve the case where the Real Statistics add-in disappears from the Add-in ribbon.
- [Real Statistics Release 4.9](https://real-statistics.com/real-statistics-release-4-9/): Describes the new features of the Real Statistics Resource Pack, an Excel add-in for statistical analysis.
- [Quick Update 26 May 2016](https://real-statistics.com/quick-update-26-may-2016/)
- [Real Statistics Release 4.8](https://real-statistics.com/release-4-8/): Describes the new features in Rel 4.8 of the Real Statistics Resource Pack, free Excel add-in for statistical analysis. Incl. Box-Cox, Mardia Test, Shapely-Owen
- [Release 4.7](https://real-statistics.com/release-4-7/): Describes the features of Release 4.7 of the Real Statistics Resource Pack, which provides a variety of statistical analysis capabilities in Excel
- [Rel 4.6 Installation](https://real-statistics.com/rel-4-6-installation/): Describes how to install Release 4.6 of the Real Statistics Resource Pack
- [Important Information about Rel 4.6](https://real-statistics.com/important-information-about-rel-4-6/): Explains that you must make sure that Solver is loaded in order to use the latest release of the Real Statistics Resource Pack.
- [Suggestion for Excel 2007 Users](https://real-statistics.com/suggestion-for-excel-2007-users/): Suggestion for Excel 2007 Users regarding installation of Real Statistics
- [Bug Fix Release 4.4.3](https://real-statistics.com/bug-fix-release-4-4-3/)
- [Real Statistics Release 4.4.2](https://real-statistics.com/real-statistics-release-4-4-2/): Describes the bug fixes in the Real Statistics Resource Pack Rel 4.4.2.
- [Website Changes](https://real-statistics.com/website-changes/): Describes some minor changes to the menus on the Real Statistics website.
- [Interpolation Changes](https://real-statistics.com/interpolation-changes/): Describes the addition of harmonic interpolation to various table lookup functions
- [Release 4.2 of Real Statistics Resource Pack](https://real-statistics.com/release-4-2-of-real-statistics-resource-pack/): Description of the latest release of the Real Statistics Resource Pack, an Excel add-in for software analysis.
- [Bug Fix Release 4.1.1 Real Statistics Resource Pack](https://real-statistics.com/bug-fix-release-4-1-1-real-statistics-resource-pack/): New release to fix a bug in the SRANK_TEST function
- [Release 4.1 of Real Statistics Resource Pack](https://real-statistics.com/release-4-1-real-statistics-resource-pack/): Describes latest release of the Real Statistics Resource Pack, an Excel add-in for statistical analysis, incl. Fligner Killeen and Jarque-Barre tests.
- [Disappearing Add-Ins Ribbon](https://real-statistics.com/disappearing-add-ins-ribbon/): Describes what causes the disappearance of the Real Statistics software option form the Add-Ins ribbon and what to do about it.
- [Release 3.8.1 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-8-1-of-the-real-statistics-resource-pack/): Announces the availability of Release 3.8.1 of the Real Statistics Resource Pack for Excel 2007 and 2010 environments.
- [Announcing Release 3.5.3 for Macintosh](https://real-statistics.com/announcing-release-3-5-3-for-macintosh/): Describes the features in the latest release of Real Statistics software for Macintosh.
- [Bug Fix Release 3.6.2](https://real-statistics.com/bug-fix-release-3-6-2/): Describes the latest release of the Real Statistics Resource Pack. Includes a fix to the hidden dialog box problem.
- [Bug Fix Release 3.6.1](https://real-statistics.com/bug-fix-release-3-6-1/): Describes the bug fixes in Release 3.6.1 of the Real Statistics Resource Pack.
- [Release 3.6 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-6-real-statistics-resource-pack/): Describes the new features in Release 3.6 of the Real Statistics Resource Pack. Includes statistical power and sample size requirements for Cronbach's Alpha.
- [Quick Update 18 Jan 2015](https://real-statistics.com/quick-update-18-jan-2015/): Describes two bug fixes to the Real Statistics Resource pack
- [Release 3.5 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-5-real-statistics-resource-pack/): Describes the new features in the latest release of the Real Statistics Resource Pack, an Excel addin used for statistical analysis.
- [Release 3.4 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-4-real-statistics-resource-pack/): Describes the new features available with Release 3.4 of the Real Statistics Resource Pack.
- [Quick Update 11 Dec 2014](https://real-statistics.com/quick-update-11-dec-2014/)
- [Release 3.3 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-3-real-statistics-resource-pack/): Describes the latest release (Rel 3.3) of the Real Statistics Resource Pack, a free statistical analysis package for use in Excel.
- [Quick Update 24 Nov 2014](https://real-statistics.com/quick-update-24-nov-2014/): Describes changes to the website, examples workbooks and software, including new Real Statistics Resource Pack Release 3.2.2
- [Release 3.2 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-2-real-statistics-software/): Describes the new capabilities in the Real Statistics Resource Pack for doing statistical analysis in Excel. Features new ANOVA and MANOVA support.
- [Quick Update for Mac Users](https://real-statistics.com/quick-update-for-mac-users/): Describes improvements to the Real Statistics Resource Pack for Mac users.
- [New Real Statistics Release for Mac Users](https://real-statistics.com/new-real-statistics-release-for-mac-users/): Announces the latest release of the Real Statistics Resource Pack for Macintosh users. This resource pack provides a wealth of statistics capabilities from within Excel
- [Quick Update 1 October 2014](https://real-statistics.com/quick-update-1-october-2014/): Describes the latest bu fixes for the Real Statistics Resource Pack.
- [Release 3.1 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-1-real-statistics-resource-pack/): Describes the latest enhancements to the Real Statistics Resource Pack, free statistics add-in for Excel.
- [Announcing Release 3.0 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-0-real-statistics-resource-pack/): Describes the new features of the Real Statistics Resource Pack
- [Release 2.17.1 Announcement](https://real-statistics.com/release-2-17-1-announcement/)
- [Quick Update 4 Sept 2014](https://real-statistics.com/quick-update-4-sept-2014/)
- [Release 2.17 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-17-of-the-real-statistics-resource-pack/): Describes new features in the Real Statistics add-in software, especially new inverse functions and statistical power functions.
- [Bug Fix Release 2.16.1](https://real-statistics.com/bug-fix-release-2-16-1/)
- [Release 2.16 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-16-real-statistics-resource-pack/): Describes the new functions in the latest release of the Real Statistics Resource Pack, an Excel statistics add-in.
- [Quick Update 26 June 2014](https://real-statistics.com/quick-update-26-june-2014/): Description of the new webpages on the Real Statistics Using Excel website.
- [Release 2.15 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-15-real-statistics-resource-pack/): Describes new features in the the Real Statistics Resource Pack Release 2.15, incl. noncentral distributions, statistical power, two-sample Kolmogorov-Smirnov.
- [Release 2.14.1 of Real Statistics Resource Pack](https://real-statistics.com/release-2-14-1-of-real-statistics-resource-pack/): Description of the mini-release, Rel 2.14.1, of the Real Statistics Resource Pack.
- [Release 2.14 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-14-of-the-real-statistics-resource-pack/): Description of the new capabilities in the Real Statistics Resource Pack and the changes to the Worksheet Examples and website.
- [Quick Update 11 May 2014](https://real-statistics.com/quick-update-11-may-2014/): All the updates to the website to describe the new features in Release 2.13.1 have now been made.
- [Quick Update 9 May 2014](https://real-statistics.com/quick-update-9-may-2014/)
- [Quick Update 7 May 2014](https://real-statistics.com/quick-update-7-may-2014/)
- [Release 2.13 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-13-real-statistics-resource-pack/): Describes the latest release of the Real Statistics Resource Pack, featuring multiple imputation (MI via FCS) and full information maximum log-likelihood (FIML)
- [Release 2.12 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-12-real-statistics-resource-pack/): Describes the latest version of the Real Statistics add-in software. It adds new features and modifies existing capabilities to better deal with missing data.
- [Release 2.11 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-11-real-statistics-resource-pack/): Describes the features of the latest release of the Real Statistics Resource Pack for use with Windows and Mac versions of Excel
- [Quick Update 17 March 2014](https://real-statistics.com/quick-update-17-march-2014/): Update on the latest capabilities on the Real Statistics website.
- [Quick Update 14 March 2014](https://real-statistics.com/quick-update-14-march-2014/): Release 2.11 is now available on Excel 2007. The webpages in the Tools menu have now been updated to support Release 2.11.
- [Quick Update 6 March 2014](https://real-statistics.com/quick-update-6-march-2014/): Describes some changes to the website, especially regarding the partial correlation coefficient and Studentized q distribution.
- [Quick Update 17 February 2014](https://real-statistics.com/quick-update-17-february-2014/): Describes improved statistical support for Excel 2011 on the Macintosh.
- [Quick Update 6 February 2014](https://real-statistics.com/quick-update-6-february-2014/): Description of new or updated webpages: Fleiss' Kappa, Runs, Binomial Distribution and Random Walks
- [Quick Update 31 Jan 2014](https://real-statistics.com/quick-update-jan-201/): Update about the new beta version of the Real Statistics Resource Pack for Mac
- [Release 2.10 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-10-real-statistics-resource-pack/): Describe new features in the Real Statistics Resource Pack: an expanded ICC function and new functions for comparing slopes and testing correlation coefficient
- [Release 2.9 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-9-real-statistics-resource-pack/): Describes the new features in the Real Statistics Resource Pack.
- [Announcing Release 2.8 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-8-real-statistics-resource-pack/): Describes the new features of the Real Statistics Resource Pack, including multinomial logistic regression support.
- [Support for Excel 2003 and older versions of Excel](https://real-statistics.com/support-for-excel-2003-and-older-versions-of-excel/)
- [Quick Update](https://real-statistics.com/quick-update/)
- [Release 2.7 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-7-real-statistics-resource-pack/): Description of the new capabilities in the Real Statistics Resource Pack, esp. ROC curve and classification table for logistic regression and weighted kappa
- [Release 2.6 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-6-of-the-real-statistics-resource-pack/): Announcing Release 2.6 of the Real Statistics Resource Pack, describing new ANOVA features and software.
- [Announcing Real Statistics Resource Pack Release 2.4](https://real-statistics.com/announcing-real-statistics-resource-pack-release-2-4/): Describes the newest features in the Real Statistics software. This software is an Excel add-in available for free download.
- [New Website Capabilities](https://real-statistics.com/new-website-capabilities/): New social media features have been added to the Real Statistics website, including a new twitter account and sharing via twitter, facebook, google+ & linkedin.
- [Other New Features in the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-1-of-the-real-statistics-resource-pack/): Description of the new features available in the Real Statistics Resource Pack, Excel add-in statistics software available for free download.
- [Announcing Release 2.3 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-3-of-the-real-statistics-resource-pack/): Description of the new features available in the Real Statistics Resource Pack, Excel add-in statistics software available for free download.
- [Announcing Release 2.2 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-2-of-the-real-statistics-resource-pack/): Description of the new features available in the Real Statistics Resource Pack, Excel add-in statistics software available for free download.
- [Announcing Release 2.0 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-0-of-the-real-statistics-resource-pack/): Announces new release of Excel add-in which adds multivariate statistics support to Real Statistics Resource Pack, including MANOVA, Hotelling's test, Box Test.
- [Announcing New Multivariate Statistics Capabilities](https://real-statistics.com/announcing-new-multivariate-statistics-capabilities/): Announcing new multivariate support for Real Statistics Using Excel.
- [Announcing Release 1.8 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-1-8-of-the-real-statistics-resource-pack/): New release of the Real Statistics Resource Pack which improves the organization of the data analysis tools and add new Outliers and Missing Data features.
- [Announcing Release 1.7 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-1-7-of-the-real-statistics-resource-pack/): Release 1.7 of the Real Statistics Resource Pack includes support for sample sizes of up to 5,000 for the Shapiro Wik test plus upgrades to data analysis tools.
- [Announcing Release 1.6](https://real-statistics.com/announcing-release-1-6/): Describes the new release of the Real Statistics Resource Pack.
- [New Releases](https://real-statistics.com/new-releases/): Describes future releases of the Real Statistics Resource Pack
- [Announcing Release 1.5](https://real-statistics.com/announcing-release-1-5/)
- [Announcing Release 1.4](https://real-statistics.com/announcing-release-1-4/)
- [Welcome to the Real Statistics Website](https://real-statistics.com/hello-world/): Request for feedback about the Real Statistics Using Excel website.

## Pages

- [Welcome](https://real-statistics.com/): Free downloadable statistics software (Excel add-in) plus comprehensive statistics tutorial for carrying out a wide range of statistical analyses in Excel.
- [CI Functions for Effect Sizes d and g](https://real-statistics.com/students-t-distribution/confidence-interval-effect-size-power/ci-functions-effect-size-d/): Describes Real Statistics functions that calculate confidence intervals for Cohen's effect size d associated with the t test in Excel.
- [Confidence Intervals for Effect Size and Power](https://real-statistics.com/students-t-distribution/confidence-interval-effect-size-power/): Describes how to calculate a confidence interval for effect size, noncentrality parameter and statistcial power for the t test in Excel. Examples and software.
- [Real Statistics Time Series Analysis Functions](https://real-statistics.com/real-statistics-environment/real-statistics-time-series-analysis-functions/): A summary of all the time series functions contained in the Real Statistics Resource Pack. A link is provided for each function to get further information.
- [Demeaning Models over Two Time Periods](https://real-statistics.com/panel-data-models/demeaning-models-over-two-time-periods/): Describes how to use demeaning to create a fixed-effects panel data model when there are two time periods. Equivalent to a differencing model.
- [Panel Data Models](https://real-statistics.com/panel-data-models/): Tutorial on how to analyze panel data using regression. Fixed effects (FEM) and random effects models (REM) are explored using Excel.
- [Econometric Data Types](https://real-statistics.com/panel-data-models/econometric-data-types/): We characterize econometric data into four types: cross-sectional, time series, pooled and panel (aka longitudinal) data. Examples of each type are provided.
- [Panel Data Analysis Tool](https://real-statistics.com/panel-data-models/panel-data-analysis-tool/): Describes how to use the Real Statistics Panel Data analysis tool to create fixed-effects and random-effects models of panel data in the Excel environment.
- [REM Example and Functions](https://real-statistics.com/panel-data-models/rem-example-and-functions/): Describes how to create a random-effects panel data model using a transformation. Excel examples and worksheet functions are described.
- [Random Effects Model (REM)](https://real-statistics.com/panel-data-models/random-effects-model-rem/): Describes how to create a random-effects panel data model using a transformation. Explains how to estimate the transformation parameter.
- [Dummy Variable Panel Model](https://real-statistics.com/panel-data-models/dummy-variable-panel-model/): Describes how to use a least-squares dummy-variable model to create a fixed-effects panel data model using Excel. Checks for differences between the units.
- [Demeaning for Panel Data](https://real-statistics.com/panel-data-models/demeaning-panel-data/): Describes how to use demeaning to create a fixed-effects panel data model even when there are more than two time periods.
- [Differencing for Panel Data](https://real-statistics.com/panel-data-models/differencing-for-panel-data/): Describes how to use differencing to create a fixed-effects panel data model even when there are more than two time periods.
- [Differencing Models over Two Time Periods](https://real-statistics.com/panel-data-models/differencing-models-two-time-periods/): Describes how to use differencing to create a fixed-effects panel data model when there are two time periods. Equivalent to a demeaning model.
- [Panel Data over Two Time Periods](https://real-statistics.com/panel-data-models/panel-data-two-time-periods/): Described fixed effects panel data models over two time periods: in particular, a description of the formatting of panel data and the regression models used.
- [Stochastic Processes](https://real-statistics.com/time-series-analysis/stochastic-processes/): Tutorial on stochastic processes, including stationary processes, white noise, random walk, autocorrelation, etc. Includes examples and Excel software.
- [Finding AR(p) coefficients](https://real-statistics.com/time-series-analysis/autoregressive-processes/finding-ar-coefficients/): Describes how to calculate in Excel the coefficients of an autoregressive process which represents a time series using ACF (Yule-Walker) and PACF
- [Characteristic Equation for AR(p) Processes](https://real-statistics.com/time-series-analysis/autoregressive-processes/characteristic-equation-autoregressive-processes/): Determine whether an autoregressive process is stationary based on properties of the characteristic equation, namely |z| > 1 for any root.
- [Autocorrelation Function](https://real-statistics.com/time-series-analysis/stochastic-processes/autocorrelation-function/): Describes how to calculate the autocorrelation function in Excel and construct correlograms. Also explains the Bartlett's, Box-Pierce and Ljung-Box tests.
- [Other Unit Root Tests](https://real-statistics.com/time-series-analysis/autoregressive-processes/other-unit-root-tests/): Describes the KPSS Test and PP Test, two unit root tests, used to determine whether a time series is stationary. Includes examples and Excel software.
- [Real Statistics ARMA Tool](https://real-statistics.com/time-series-analysis/arma-processes/real-statistics-arma-tool/): Describes how to build an ARMA model of a time series in Excel and use this model to create a forecast. Examples and an Excel add-in are included.
- [Desc - QQ and Dot Plots](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/desc-qq-and-dot-plots/): Describes in detail the QQ Plot and Dot Plot options of Real Statistics' Excel-based Descriptive Statistics and Normality data analysis tool.
- [Desc - Shapiro-Wilk Test](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/desc-shapiro-wilk-test/): Describes in detail the Shapiro-Wilk option of Real Statistics' Excel-based Descriptive Statistics and Normality data analysis tool.
- [Desc - Box Plots](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/desc-box-plots/): Describes in detail the Box Plot and Box Plot w/ Outliers options of Real Statistics' Excel-based Descriptive Statistics and Normality data analysis tool.
- [Desc - Grubbs' Test](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/desc-grubbs-test/): Describes in detail the Grubbs' Test option of Real Statistics' Excel-based Descriptive Statistics and Normality data analysis tool.
- [McNemar-Bowker Test](https://real-statistics.com/non-parametric-tests/mcnemar-bowker-test/): Describes how to conduct the McNemar-Bowker Test in Excel. An example is provided, as well as software and the appropriate spreadsheet
- [Complex Matrices in Excel Format](https://real-statistics.com/other-mathematical-topics/complex-matrices-in-excel-format/): Describes how to perform various operations in Excel on matrices with complex entries of the form "a+bi", i.e. text versions of complex numbers used in Excel.
- [Real Statistics Ordinal Regression Support](https://real-statistics.com/ordinal-regression/real-statistics-ordinal-regression-support/): Describes how to use Real Statistics functions and data analysis tools to create an ordinal regression model in Excel and use it to make predictions.
- [Weibull with Censored Data](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/weibull-censored-data/): Describes how to estimate Weibull distribution parameters that best fit a data set when there is censored data. Uses MLE + Newton's method. Example & software.
- [Forecasting using an ARMA model](https://real-statistics.com/time-series-analysis/arma-processes/forecasting-arma/): Describes how to build a forecast for a time series based on an ARMA model. We show how to do this using a specific example in Excel.
- [Spline Fitting and Interpolation](https://real-statistics.com/other-mathematical-topics/spline-fitting-interpolation/): Describes how to create a (cubic) spline curve that fits a series of data points. An example in given in Excel that shows how to do this in detail.
- [Calculate ARMA(p,q) coefficients using maximum likelihood](https://real-statistics.com/time-series-analysis/arma-processes/arma-coefficients-maximum-likelihood/): Describes how to use maximum likelihood estimation (MLE) techniques to calculate the coefficients of an autoregression moving average process, ARMA(p,q).
- [Poisson Regression Residuals and Goodness of Fit](https://real-statistics.com/poisson-regression/poisson-regression-residuals-and-goodness-of-fit/): Describes how to calculate the residuals for a Poisson regression model and the goodness of fit statistics in Excel. Examples and software are furnished.
- [ARMA Proofs](https://real-statistics.com/time-series-analysis/arma-processes/arma-proofs/): Presents mathematical proofs of properties in the ARMA Processes portion of the website. These proofs don't require knowledge of calculus.
- [Nemenyi Test after KW](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/nemenyi-test-after-kw/): Describes how to conduct the Nemenyi test after a significant Kruskal-Wallis test. Excel examples and software are included.
- [Contrasts post KW](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/contrasts-post-kw/): Describes how to conduct the contrasts tests after a significant Kruskal-Wallis test. Excel examples and software are included.
- [Dunn's Test after KW](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/dunns-test-after-kw/): Describes how to conduct Dunn's test after a significant Kruskal-Wallis test. Excel examples are included and Excel functionality described.
- [Real Statistics KS Test for Normality](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/lilliefors-test-normality/real-statistics-ks-test-for-normality/): Describes how to perform the Kolmogorov-Smirnov test for normality in Excel, especially when the mean and standard deviation are estimated from the data.
- [Proportional Odds Model Proofs](https://real-statistics.com/ordinal-regression/proportional-odds-model/proportional-odds-model-proofs/): Provides the proofs of Properties 1 and 2 which show how to calculate the ordinal regression coefficients for the proportional odds model using Newton's method.
- [Beta Conjugate Prior](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/beta-conjugate-prior/): Describes how to calculate the (beta) posterior pdf for binomially distributed data with a beta prior. Includes Excel examples and software.
- [Real Statistics Support for Spline Fit](https://real-statistics.com/other-mathematical-topics/spline-fitting-interpolation/spline-real-statistics-support/): Describes the Real Statistics functions and data analysis tool that support fitting a spline curve to data points in Excel. An example is provided.
- [Real Statistics Support for Logistic Regression](https://real-statistics.com/logistic-regression/real-statistics-support-for-logistic-regression/): Describes the data analysis tools for logistic regression supplied by the Real Statistics add-in to Excel for statistical analysis.
- [Correlogram](https://real-statistics.com/time-series-analysis/stochastic-processes/correlogram/): Describes how to construct an ACF correlogram and PACF correlogram in Excel that includes confidence intervals. Examples and software are provides.
- [Miscellaneous Time Series Topics](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/): Describes additional topics for Time Series analysis, including Mann-Kendall test, Sen's slope, Granger causality, cointegration, cross-correlations, ARIMAX.
- [Moving Average Proofs](https://real-statistics.com/time-series-analysis/moving-average-processes/moving-average-proofs/): Provides the proofs of various properties about finite Moving Average (MA) Processes, as well as infinite Moving Average processes.
- [Time Series Analysis](https://real-statistics.com/time-series-analysis/): Tutorial on time series analysis in Excel. Includes examples and software for moving average, exponential smoothing, Holt and Holt-Winters, ARIMA (Box-Jenkins).
- [Calculating MA Coefficients using ACF](https://real-statistics.com/time-series-analysis/moving-average-processes/ma-coefficients-acf/): We describe how to estimate the coefficients of a Moving Average MA(q) model of a time series in Excel using the ACF. We also include examples in Excel.
- [Calculating MA Coefficients using Solver](https://real-statistics.com/time-series-analysis/moving-average-processes/calculating-ma-coefficients-solver/): Describes how to build an MA(q) model of a time series in Excel using Solver. An example is given of how to calculate the model coefficients
- [Infinite Moving Average Processes](https://real-statistics.com/time-series-analysis/moving-average-processes/infinite-moving-average-processes/): Describes how to calculate the psi coefficients in Excel for an infinite moving averages process which represents an ARMA process. Incl. examples and software.
- [MA(q) Process Basic Concepts](https://real-statistics.com/time-series-analysis/moving-average-processes/ma-process-basic-concepts/): Describes key properties of moving average processes and time series, and shows how to simulate an MA(q) process in Excel.
- [Moving Average Processes](https://real-statistics.com/time-series-analysis/moving-average-processes/): Tutorial on moving average (MA) process. Describes how to find ACF and MA coefficients in Excel. Excel worksheet functions and examples are provided.
- [Finding AR(p) coefficients using Regression](https://real-statistics.com/time-series-analysis/autoregressive-processes/finding-ar-coefficients-using-regression/): Describes how to calculate the coefficients of an AR(p) process that represents time series using linear regression in Excel. Examples and software are provided
- [Lag Function](https://real-statistics.com/time-series-analysis/autoregressive-processes/lag-function/): Describes the lag function (aka backshift operator) and how to represent an autoregressive process using the lag function.
- [Partial Autocorrelation for AR(p) Process](https://real-statistics.com/time-series-analysis/autoregressive-processes/partial-autocorrelation-for-arp-process/): Provides graphs of the partial correlation function of autoregressive processes and describes the connection with the process coefficients
- [ARMA Processes](https://real-statistics.com/time-series-analysis/arma-processes/): Tutorial on autoregressive moving average processes, including how to build ARMA models in Excel and use them for forecasting. Software and examples included.
- [Mixed Factor Nested Design](https://real-statistics.com/anova-random-nested-factors/nested-anova/mixed-nested-design/): Describes the basic concepts of a nested ANOVA model with one fixed factor and one random factor. Includes key formulas used to create the model.
- [Fixed Factor Nested ANOVA](https://real-statistics.com/anova-random-nested-factors/nested-anova/fixed-factor-nested-anova/): Describes the basic concepts of a nested ANOVA model with two fixed factors. We also provide an Excel-based data analysis tool for performing this analysis.
- [Random Factor Nested ANOVA](https://real-statistics.com/anova-random-nested-factors/nested-anova/random-factor-nested-anova/): Describes the basic concepts of a nested ANOVA model with two random factors. We also provide an Excel-based data analysis tool for performing this analysis.
- [Anova with Random or Nested Factors](https://real-statistics.com/anova-random-nested-factors/): Describes how to construct Anova models with random, nested, or mixed factors in Excel. Includes software and a number of examples
- [Two Mixed Factors ANOVA](https://real-statistics.com/anova-random-nested-factors/two-factor-mixed-anova/): Describes how to calculate ANOVA for one fixed factor and one random factor (mixed model) in Excel. Examples and software provided.
- [Two Random Factors ANOVA](https://real-statistics.com/anova-random-nested-factors/two-random-factors-anova/): Describes how to calculate ANOVA for two random factors in Excel. Excel examples are provided as is a data analysis tool for doing this.
- [Real Statistics Support for SARIMA](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/real-statistics-support-for-sarima/): Describes how to to use the Real Statistics SARIMA data analysis tool to create a SARIMA model and forecast in Excel. The process is illustrated via an example.
- [SARIMA Forecast Example](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/sarima-forecast-example/): Shows how to create a SARIMA forecast based on Amazon quarterly revenues. The webpage shows how to build the forecast, step-by-step in Excel.
- [SARIMA Model Example](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/sarima-example/): Shows how to create a SARIMA model (for Amazon revenues), step by step, in Excel using ordinary differencing as well as seasonal differencing.
- [SARIMA Models](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/sarima-models/): Defines a seasonal ARIMA (SARIMA) model and describes the formulas used to create a forecast based on this type of time series model.
- [Seasonality for Time Series](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/seasonality/): Describes seasonality for time series. Extends notions of random walk, drift, etc. to time series with seasonality. Three approaches are described
- [Seasonal ARIMA (SARIMA)](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/): This part of the Real Statistics website provides a tutorial on Seasonal ARIMA modelling and forecasting. Excel examples and software are provided.
- [ARIMA Forecasting](https://real-statistics.com/time-series-analysis/arima-processes/arima-forecasting/): Describes how to use the Real Statistics data analysis tool to perform ARIMA forecasts based on Excel's Solver. Software and examples are included.
- [Comparing ARIMA Models](https://real-statistics.com/time-series-analysis/arima-processes/comparing-arima-models/): Describes how to compare ARIMA (Box-Jenkins) models in Excel using Akaike Information Criterion (AIC) and Bayesian Information Criteria (BIC). Incl. example.
- [ARIMA Model Coefficients](https://real-statistics.com/time-series-analysis/arima-processes/arima-model-coefficients/): Describes how to use Excel's Solver to find model coefficients for a specified ARIMA(p,q,d) model. Software and examples are also provided.
- [ARIMA Identification](https://real-statistics.com/time-series-analysis/arima-processes/arima-identification/): Describes approaches to fit time series data to an appropriate ARIMA process (i.e. determine the p, q, d parameters) via plotting and ACF and PACF.
- [ARIMA Processes](https://real-statistics.com/time-series-analysis/arima-processes/): Describes how to find an ARIMA process in Excel which best fits time series data. Includes Box-Jenkins approach, examples and software.
- [Calculate ARMA(p,q) coefficients using Solver](https://real-statistics.com/time-series-analysis/arma-processes/arma-coefficients-solver/): Describes how to use Solver to calculate the coefficients of an ARMA(p,q) process or time series. Examples and software are provided.
- [ARMA(p,q) Processes](https://real-statistics.com/time-series-analysis/arma-processes/arma-pq-processes/): Describes some key properties of (stationary and invertible) autoregression moving average (ARMA) processes and time series.
- [ARMA Processes Basic Concepts](https://real-statistics.com/time-series-analysis/arma-processes/arma-processes-basic-concepts/): Description of some of the basic concepts about autoregressive moving average (ARMA) processes and time series based on the backshift operator.
- [ARMA(1,1) Processes](https://real-statistics.com/time-series-analysis/arma-processes/arma11-processes/): Describes the basic characteristics of an ARMA(1,1) process, including mean, variance and autocorrelation (ACF). Examples and software is provided.
- [Evaluating the ARMA model](https://real-statistics.com/time-series-analysis/arma-processes/evaluating-the-arma-model/): Describes how to evaluate an ARMA model by using descriptive statistics, significance testing of model coefficients and use of AIC and BIC statistics.
- [ARMA Tool Options](https://real-statistics.com/time-series-analysis/arma-processes/arma-tool-options/): Demonstrates how to use various options of the Real Statistics ARIMA data analysis tool to build an ARMA model in Excel and use it for forecasting.
- [Autoregressive Processes Basic Concepts](https://real-statistics.com/time-series-analysis/autoregressive-processes/autoregressive-processes-basic-concepts/): Describes key properties of autoregressive processes and time series, including the Yule-Walker equations, and shows how to simulate an AR(p) process in Excel.
- [Gaussian Mixture Models](https://real-statistics.com/multivariate-statistics/gaussian-mixture-models/): Tutorial on Gaussian Mixture Models (GMM) and how to construct them in Excel using the EM algorithm. Examples examples and software tools are provided.
- [Real Statistics Univariate GMM Support](https://real-statistics.com/multivariate-statistics/gaussian-mixture-models/real-statistics-univariate-gmm-support/): Describes the worksheet functions and data analysis tools provided by the Real Statistics software to create and utilize univariate GMM models in Excel.
- [Real Statistics Multivariate GMM Support](https://real-statistics.com/multivariate-statistics/gaussian-mixture-models/real-stats-multivariate-gmm-support/): Describes the worksheet functions and data analysis tools provided by the Real Statistics software to create and utilize multivariate GMM models in Excel.
- [GMM Example](https://real-statistics.com/multivariate-statistics/gaussian-mixture-models/gmm-example/): Shows how to create a Gaussian Mixture model in Excel. Am example is provided and the step-by-step procedure is explained.
- [Autoregressive Processes](https://real-statistics.com/time-series-analysis/autoregressive-processes/): Tutorial on autoregressive processes and time series, including examples in Excel and software. Describes how to build AR(p) models and create forecasts.
- [Time Series Testing Tools](https://real-statistics.com/time-series-analysis/stochastic-processes/time-series-testing-tools/): Describes how to use the Real Statistics Time Series Testing data analysis tools in Excel to compute ACF/PACF, and conduct ADF, Ljung-Box and Bartlett's tests.
- [Deterministic Trend](https://real-statistics.com/time-series-analysis/stochastic-processes/deterministic-trend/): Describes the characteristics of linear deterministic trend time series and how to detrend them in Excel to create a stationary time series.
- [Calculating Orthogonal Polynomial Contrast Coefficients](https://real-statistics.com/one-way-analysis-of-variance-anova/trend-analysis-polynomial-contrast-coefficients/calculating-orthogonal-polynomial-contrast-coefficients/): Describes how to calculate the orthogonal polynomial contrast coefficients for equally-spaced groups in Excel. Shows hoe to build coefficient tables
- [Random Walk](https://real-statistics.com/time-series-analysis/stochastic-processes/random-walk/): Describes random walk time series and their characteristics using Excel capabilities. Explains how to test for a random walk.
- [Multivariate GMM](https://real-statistics.com/multivariate-statistics/gaussian-mixture-models/multivariate-gmm/): Describes how to build a Gaussian Mixture Models (GMM) for multivariate data using the EM algorithm. This model can be used for cluster analysis.
- [Purely Random Time Series](https://real-statistics.com/time-series-analysis/stochastic-processes/purely-random-time-series/): Describes purely random (white noise) time series. Shows how to test for white noise in Excel and describes their characteristics.
- [Polynomial Regression Models based on Trend Analysis](https://real-statistics.com/one-way-analysis-of-variance-anova/trend-analysis-polynomial-contrast-coefficients/polynomial-regression-models-trend-analysis/): Describes how to create polynomial regression models using orthogonal contrast coefficients. Also shows how to construct tables of such coefficients in Excel.
- [Partial Autocorrelation Function](https://real-statistics.com/time-series-analysis/stochastic-processes/partial-autocorrelation-function/): Describes how to calculate the partial autocorrelation function in Excel. Examples are provided as well as Excel worksheet functions.
- [Univariate GMM](https://real-statistics.com/multivariate-statistics/gaussian-mixture-models/univariate-gmm/): Describes how to build a Gaussian Mixture Models (GMM) for univariate data using the EM algorithm. This model can be used for cluster analysis.
- [BGFS Algorithm](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/bgfs-algorithm/): Describes the BGFS algorithm for finding local minima of a multivariate function. Examples and Excel software are provided.
- [Two Factor ANOVA without Replication](https://real-statistics.com/two-way-anova/two-factor-anova-without-replication/): Describes how to perform two-way ANOVA in Excel using the standard Excel data analysis tool and worksheet functions. Also describes Real Statistics' tool.
- [Multivariate Normality Functions](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-normality-functions/): Describes how to calculate the cdf and pdf of the bivariate normal distribution in Excel as well as the Mahalanobis distance between two vectors
- [Stationary Process](https://real-statistics.com/time-series-analysis/stochastic-processes/stationary-process/): Defines stationary stochastic processes and time series. Describes some characteristics of stationary processes. Gives examples in Excel.
- [Real Statistics Non-Parametric Test Functions](https://real-statistics.com/real-statistics-environment/non_parametric-test-functions/): Summary of worksheet functions contained in the Real Statistics Resource Pack that support non-parametric tests. Includes statistical table lookup functions.
- [Order statistics from continuous uniform population](https://real-statistics.com/other-key-distributions/uniform-distribution/distribution-of-order-statistics-from-continuous-population/): Describes order statistics from a uniform population and how they are distributed. Includes properties and provides a number of examples using Excel.
- [Random Walk Metropolis Algorithm](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/markov-chain-monte-carlo/random-walk-metropolis-algorithm/): Describes how to use the Random Walk Metropolis Algorithm for data that follows a binomial distribution. Includes Excel examples and software
- [Normal Confidence Intervals for Percentiles](https://real-statistics.com/order-statistics/confidence-intervals-order-statistics/normal-confidence-intervals-for-percentiles/): Describes how to determine the confidence Intervals for percentiles using a normal distribution approximation. A number of examples in Excel are provided.
- [Confidence Interval for Quartiles and Percentiles](https://real-statistics.com/order-statistics/confidence-intervals-order-statistics/confidence-intervals-for-percentiles/): Describes how to determine the confidence Intervals for percentiles using Excel. A number of examples in Excel are provided.
- [Confidence Intervals for Order Statistics, Medians and Percentiles](https://real-statistics.com/order-statistics/confidence-intervals-order-statistics/): Describes how to determine the confidence Intervals for order statistics, medians and percentiles using Excel. A variety of approaches and examples are provided
- [Real Statistics Multivariate Functions](https://real-statistics.com/real-statistics-environment/real-statistics-multivariate-functions/): Summary of all the multivariate statistics functions contained in the Real Statistics Resource Pack, an Excel add/in that supports statistical analysis
- [Poisson Regression Proofs](https://real-statistics.com/poisson-regression/poisson-regression-proofs/): Provides the proofs of properties related to Newton's method for estimating the Poisson regression coefficients and their standard errors. Requires calculus.
- [Holt-Winters Additive Method](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/holt-winters-additive/): Tutorial on seasonal forecasting using an additive model in Excel. Examples and software are provided. Also explains how to use Solver to optimize forecasts
- [Uniform Distribution Proofs](https://real-statistics.com/other-key-distributions/uniform-distribution/uniform-distribution-proofs/): Provides the proofs of various properties about the uniform distribution and related distributions. Calculus is required for this webpage.
- [Ordered Independence Test Tool](https://real-statistics.com/correlation/ordered-chi-square-independence-test/ordered-independence-test-tool/): Shows how to conduct a test for independence with ordered data using the Real Statistics Resource Pack, and Excel add-in for statistical analysis
- [Gini Coefficient](https://real-statistics.com/non-parametric-tests/gini-coefficient/): Describes the Gini coefficient (aka Gini index), and explains how it is used and how it is calculated, including the relevant formulas.
- [Two-way MANOVA Example](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/two-way-manova-example/): Provides an example of how to perform two-way MANOVA in Excel. An Excel-based data analysis tool is also provided to make it easier to do this.
- [More Pretest-Posttest Design](https://real-statistics.com/analysis-of-covariance-ancova/pretest-posttest-design/more-pretest-posttest-design/): Describes how to perform pretest-posttest analysis when there are more than two between-subjects groups. Excel examples are provided.
- [Cronbach's Alpha Basic Concepts](https://real-statistics.com/reliability/internal-consistency-reliability/cronbachs-alpha/cronbachs-alpha-basic-concepts/): Describes how to calculate Cronbach's alpha coefficient for reliability in Excel by using a technique similar to that for KR20 as well as by using ANOVA.
- [Cohen's Kappa Sample Size](https://real-statistics.com/reliability/interrater-reliability/cohens-kappa/cohens-kappa-sample-size/): Describes how to calculate the power and minimum sample size required for Cohen's kappa in the case where there are two categories.
- [Lorenz Curve](https://real-statistics.com/non-parametric-tests/gini-coefficient/lorenz-curve/): Provides step-by-step instructions on how to create a Lorenz curve in Excel. Describes the relationship between the Lorenz curve and the Gini index.
- [Passing-Bablok Regression Basic Concepts](https://real-statistics.com/regression/passing-bablok-regression/passing-bablok-regression-basic-concepts/): Provides an overview of Passing-Bablok regression and gives a detailed example of how to implement this type of regression in Excel.
- [PERT Distribution](https://real-statistics.com/binomial-and-related-distributions/pert-distribution/): Describes how to calculate the pdf and cdf of the PERT distribution in Excel. Also shows how to create a graph of the PERT distribution in Excel.
- [WLS regression and heteroskedasticity](https://real-statistics.com/multiple-regression/weighted-linear-regression/wls-regression-and-heteroskedasticity/): Describes how to address heteroskedasticity by using weighted least-squares (WLS) regression. Numerous examples are given. Excel software is provided.
- [Weighted Regression Basics](https://real-statistics.com/multiple-regression/weighted-linear-regression/weighted-regression-basics/): Describes the basic characteristics of weighted linear regression. Explains how to perform this type of regression in Excel. Examples are provided,
- [Multiple Solutions to Linear Equations](https://real-statistics.com/matrices-and-iterative-procedures/multiple-solutions-to-linear-equations/): Describes how to specify the solutions as a linear combination of vectors to simultaneous linear equations even when there is an infinite number of solutions.
- [Bibliography](https://real-statistics.com/appendix/bibliography/): Provides a list of various references used throughout the Real Statistics website on a variety of statistical subjects. Where available a link is included.
- [Pairwise Mann-Whitney Tests](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/pairwise-mann-whitney-tests/): Describes how to conduct the pairwise Mann-Whitney tests after a significant Kruskal-Wallis test. Excel examples and software are included.
- [Conover Test after KW](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/conover-test-after-kw/): Describes how to conduct the Conover test after a significant Kruskal-Wallis test. Excel examples and software are included.
- [Schaich-Hamerle Test after KW](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/schaich-hamerle-test/): Describes how to conduct the Schaich-Hamerle test after a significant Kruskal-Wallis test. Excel examples and software are included.
- [Paired Sample Sign Test](https://real-statistics.com/non-parametric-tests/sign-test/paired-sample-sign-test/): Describes how to use the sign test to perform a paired samples test when the assumptions for a t test are not met, Examples in Excel and software are provided,
- [White Test for Heteroskedasticity](https://real-statistics.com/multiple-regression/heteroskedasticity/white-test-for-heteroskedasticity/): Describes the White test and how to use it to test the homoskedasticity assumption of linear regression. We provide an example and Excel worksheet functions.
- [Breusch-Pagan Test](https://real-statistics.com/multiple-regression/heteroskedasticity/breusch-pagan-test/): Describes how to conduct the Breusch-Pagan test in Excel to test for homoskedasticity. We also provide an example and Excel worksheet functions.
- [Heteroskedasticity Data Analysis Tool](https://real-statistics.com/multiple-regression/heteroskedasticity/heteroskedasticity-data-analysis-tool/): Describes how to use the Real Statistics Heteroskedasticity data analysis tool in Excel to perform the Breusch-Pagan and White tests.
- [Rasch Analysis Support](https://real-statistics.com/reliability/item-response-theory/rasch-analysis-support/): Describes how to build a Rasch model (via the dichotomous UCON method) in Excel using the Real Statistics statistical analysis software.
- [Bairstow's Method](https://real-statistics.com/other-mathematical-topics/roots-of-a-polynomial/bairstows-method/): Describes how to carry out Bairstow's Method to find roots of a polynomial in Excel. Examples are included. We also show how to find the roots using Solver.
- [T-test Analysis Tool](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/t-test-analysis-tool/): Describes how to use the Real Statistics data analysis tool to conduct a two independent sample t-test in Excel. Examples are provided.
- [Linear Combination of Coefficients](https://real-statistics.com/multiple-regression/constrained-linear-regression/linear-combination-of-coefficients/): Describes how to identify in Excel linear regression coefficients whose linear combination is equal to some constant. Examples and software are included.
- [MST for points in r-space](https://real-statistics.com/other-mathematical-topics/graph-theory/mst-points-in-r-space/): Describes how to create a minimum spanning tree for points in r-space using weighted and unweighted Minkowski distance. Includes examples & software in Excel.
- [Triangular Distribution](https://real-statistics.com/other-key-distributions/uniform-distribution/triangular-distribution/): Describes how to calculate the pdf and cdf of the triangular distribution in Excel. Key properties of this distribution are also described.
- [Granger Causality](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/granger-causality/): Shows how to test in Excel whether one time series Granger-causes another time series. Examples and software are included
- [Normal Conjugate Priors Proofs](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/conjugate-priors-normal-distribution/normal-conjugate-priors-proofs/): Proofs regarding the normal conjugate priors: (1) mean unknown and variance known, (2) variance unknown and mean known and (3) mean and variance are unknown.
- [Polar Coordinates and Roots of a Complex Number](https://real-statistics.com/other-mathematical-topics/polar-coordinates-complex-roots/): How to convert complex numbers from rectangular to polar form and vice versus in Excel. Also, how to find the nth roots of a real or complex number using Excel.
- [Cliff's Delta](https://real-statistics.com/non-parametric-tests/mann-whitney-test/cliffs-delta/): Describes how to calculate Cliff's Delta non-parametric effect size in Excel. Includes examples and an Excel worksheet function.
- [Prime Numbers](https://real-statistics.com/other-mathematical-topics/prime-numbers/): Describes how to determine whether a number is prime in Excel. Also shows how to create the prime factorization of an integer.
- [Proportion Testing Analysis Tools](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/proportion-testing-analysis-tools/): How to use Real Statistics data analysis tools & functions to perform one- and two-sample proportion testing in Excel. Incl. confidence interval & effect size.
- [Two Sample (Equal Variances) Effect Size](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/two-sample-effect-size/): Describes how to calculate a 1-alpha confidence interval for Cohen effect size d for a two-sample test using the Hedges and Olkin method.
- [Bayesian Distributions](https://real-statistics.com/other-key-distributions/miscellaneous-distributions/): Describes the inverse gamma and (scaled) inverse chi-square distributions, which are useful in Bayesian statistics, and how to calculate them in Excel.
- [Exponential Smoothing Confidence Interval](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/simple-exponential-smoothing/exponential-smoothing-confidence-interval/): Describes how to calculate the standard error and confidence interval of a forecast obtained via Simple Exponential Smoothing. Example and software are provided
- [Steel Test after KW](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/steel-test-after-kw/): Describes how to conduct the Steel test after a significant Kruskal-Wallis test. Excel examples and software are included.
- [Conjugate Priors Normal Distribution](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/conjugate-priors-normal-distribution/): Describes the conjugate priors for normal data: (1) mean unknown and variance known, (2) variance unknown and mean known and (3) mean and variance are unknown.
- [Bayesian Statistics](https://real-statistics.com/bayesian-statistics/): Provides a tutorial on Bayesian Statistics. Includes examples using Excel and worksheet functions and data analysis tools accessible from Excel.
- [Data Conversion and Reformatting](https://real-statistics.com/real-statistics-environment/data-conversion/): Reformatting data in Excel (sorting, resizing, removing empty cells, deleting missing data, etc.) and converting from raw sample data to a frequency table.
- [Total Least Squares Regression](https://real-statistics.com/multiple-regression/total-least-squares-regression/): Describes how to perform total least squares regression in Excel by using Singular Value Decomposition (SVD). Examples and software are included.
- [Tukey HSD (Honestly Significant Difference)](https://real-statistics.com/one-way-analysis-of-variance-anova/unplanned-comparisons/tukey-hsd/): Describes how to perform the Tukey HSD post-hoc test in Excel following a significant one-way ANOVA result. Examples and software are provided.
- [Frequency Table Conversion](https://real-statistics.com/real-statistics-environment/data-conversion/frequency-table-conversion/): Describes how to convert a frequency table to individual sample values and vice versa in Excel. Also presents Real Statistics functions that simplify the task.
- [One Sample Effect Size](https://real-statistics.com/students-t-distribution/one-sample-t-test/one-sample-effect-size/): Describes the effect size for a one-sample t-test and how to calculate a 1-alpha confidence interval for Cohen effect size d using the Hedges and Olkin method.
- [Diebold-Mariano Test](https://real-statistics.com/time-series-analysis/forecasting-accuracy/diebold-mariano-test/): Describes how to determine in Excel whether two time-series forecasts have significantly different accuracy by using the Diebold-Mariano test or HLN Test.
- [Graphical Tests for Heteroskedasticity](https://real-statistics.com/multiple-regression/heteroskedasticity/graphical-tests-for-heteroskedasticity/): Describes how to determine whether data meets the homoskedasticity assumption for linear regression using graphical techniques. Excel example is provided.
- [Bounded Regression Coefficients](https://real-statistics.com/multiple-regression/constrained-linear-regression/bounded-regression-coefficients/): Describes how to determine the coefficients of a linear regression model that is subject to lower and/or upper bounds. Examples and software are provided.
- [Coefficient of Variation Testing](https://real-statistics.com/students-t-distribution/coefficient-of-variation-testing/): Describes how to conduct one-sample and two-sample testing of the coefficient of variation in Excel. Software and examples are provided.
- [Pretest-Posttest Design using ANCOVA](https://real-statistics.com/analysis-of-covariance-ancova/pretest-posttest-design/pretest-posttest-design-using-ancova/): Describes how to use ANCOVA for pretest-posttest analysis. Includes an Excel example and explains how to perform the analysis in Excel.
- [Lp estimate via Newton's method](https://real-statistics.com/descriptive-statistics/lp-estimators/lp-estimate-via-newtons-method/): Describes how to calculate the Lp robust estimate of central tendency using Newton's iterative method to find a solution.
- [Proportional Odds Model](https://real-statistics.com/ordinal-regression/proportional-odds-model/): Describes how to build an ordinal logistic regression model using the proportional odds model via Newton's method for minimizing the log-likelihood function.
- [Cochran-Armitage Test](https://real-statistics.com/chi-square-and-f-distributions/cochran-armitage-test/): Describes how to conduct the Cochran-Armitage test in Excel which determines whether there is a linear trend for proportional data An example is included.
- [Lp Estimators](https://real-statistics.com/descriptive-statistics/lp-estimators/): Describes the Lp-estimator as a robust measure of central tendency and how to calculate it in Excel. Also describes the Minkowski distance.
- [Cubic Polynomials](https://real-statistics.com/other-mathematical-topics/roots-of-a-polynomial/cubic-polynomials/): Describes how to find the (real and complex) roots of a cubic polynomial using the cubic formula in Excel. An Excel function is also provided to get these roots
- [EM Algorithm Bivariate Normal Data](https://real-statistics.com/handling-missing-data/em-algorithm/em-algorithm-bivariate-normal-data/): Describes the EM algorithm and shows how to use it in Excel with bivariate normally distributed data with missing data elements.
- [Method of Moments: Real Statistics Support](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-real-statistics-support/): Describes Excel worksheet functions found in the Real Statistics Resource Pack for distribution fitting using the method of moments
- [Weighted Mean and Median](https://real-statistics.com/descriptive-statistics/measures-central-tendency/weighted-mean-and-median/): Defines the weighted mean and weighted median and describes how to calculate the weighted mean and weighted median in Excel.
- [Poisson Regression Predictions](https://real-statistics.com/poisson-regression/poisson-regression-predictions/): Describes how to make predictions in Excel using a Poisson Regression model. Examples and Excel worksheet functions for doing this are provided.
- [Kruskal Algorithm (MST)](https://real-statistics.com/other-mathematical-topics/graph-theory/kruskal-algorithm-mst/): Describes the Kruskal algorithm for creating a minimum spanning tree (MST) of a connected graph using Excel. Examples and software are included.
- [GLS Method for Autocorrelation](https://real-statistics.com/multiple-regression/autocorrelation/gls-method-for-autocorrelation/): Describes the general least squares (GLS) approach to regression. This is useful when there is autocorrelation. Includes the Prais-Winsten transformation.
- [Gibbs Sampler Normal Distribution](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/gibbs-sampler-normal-distribution/): Describes how to use Gibbs Sampler to create a sample for the bivariate normal distribution. An example in Excel is provided.
- [Goodness of Fit Analysis Tools](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-analysis-tools/): Describes how to use the Real Statistics Goodness of Fit Analysis Tools. These tools work in Excel and can be used free of charge
- [Monte Carlo Simulation Normal Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/monte-carlo-simulation-normal-data/): Provides step-by-step examples of using Monte Carlo simulation in Excel based on conjugate priors for normally distributed data.
- [Bayesian Statistics for Normal Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/): Tutorial on how to use Bayesian statistics techniques where the data follows a normal distribution. Examples are provided using Excel
- [Geometric Distribution Examples](https://real-statistics.com/binomial-and-related-distributions/negative-binomial-and-geometric-distributions/geometric-distribution-examples/): Presents a variety of examples of how to use the geometric distribution. The solutions to these examples are provided using Excel.
- [Polynomial Regression Analysis Tool](https://real-statistics.com/multiple-regression/polynomial-regression/polynomial-regression-analysis-tool/): Describes how to use the Real Statistics software to create polynomial regression models in Excel. Software and examples are provided.
- [Tetrachoric Correlation Estimation](https://real-statistics.com/correlation/polychoric-correlation/tetrachoric-correlation-estimation/): Describes how to estimate the terachoric correlation coefficient in Excel. Two algorithms are provided, along with standard error and confidence intervals.
- [One-Sample Anderson-Darling Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/anderson-darling-test/): Describes how to perform a one-sample Anderson-Darling test for normal, exponential, gamma, Weibull, etc. distributions in Excel. Examples & software provided.
- [Real Statistics Capabilities for Multiple Regression](https://real-statistics.com/multiple-regression/multiple-regression-analysis/real-statistics-capabilities-for-multiple-regression/): Describes the capabilities provided by the Real Statistics Resource Pack in support of multiple regression. Software and examples provided.
- [Two Factor Multivariate Repeated Measures](https://real-statistics.com/multivariate-statistics/multivariate-repeated-measures-tests/two-factor-multivariate-repeated-measures/): Describes how to perform two a two factor repeated measures test using multivariate techniques (MANOVA) in Excel without the sphericity assumption.
- [LU Factorization](https://real-statistics.com/linear-algebra-matrix-topics/lu-factorization/): Describes how to perform an LU factorization (aka LU decomposition) of a square matrix in Excel. Examples and software are provided.
- [Statistical Power for the Binomial Distribution](https://real-statistics.com/binomial-and-related-distributions/statistical-power-binomial-distribution/): Description of how to calculate the power of a one-sample and two-sample hypothesisi testing using the binomial distribution. Examples are given.
- [Network Diagrams in Excel](https://real-statistics.com/other-mathematical-topics/graph-theory/network-diagrams-in-excel/): Describes how to construct network diagrams for undirected graphs that connect pairs (x,y) of points in Excel using a Real Statistics data analysis tool.
- [Graph Theory](https://real-statistics.com/other-mathematical-topics/graph-theory/): Provides a tutorial on some graph theory topics, especially on how to construct a minimum spanning tree for a connected undirected, weighted graph in Excel.
- [Mac User Interface](https://real-statistics.com/real-statistics-environment/mac-user-interface/): Describes differences between the Windows and Mac user interface to the Real Statistics data analysis tools. Examples are provided
- [Lp Regression](https://real-statistics.com/multiple-regression/lp-regression/): Describes how to conduct Lp regression in Excel based on the Lp norm for values of p between 1 and 2. When p = 1 Lp regression is equivalent to LAD regression.
- [Complex Number Matrices](https://real-statistics.com/other-mathematical-topics/complex-matrices/): Describes how to perform matrix operations in Excel for matrices which contain complex number values, Includes examples and Excel addin.
- [Method of Moments: Pareto Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-pareto-distribution/): Describes how to estimate the alpha and m parameters of the Pareto distribution that fits a set of data using the method of moments in Excel.
- [Complex Linear Equations](https://real-statistics.com/other-mathematical-topics/complex-linear-equations/): Describes how to solve a system of linear equations with complex coefficients. Examples using Excel are provided as well as Excel software.
- [Required Sample Size for Binomial Testing](https://real-statistics.com/binomial-and-related-distributions/required-sample-size-binomial-testing/): Description of how to calculate the sample size required for on-sample hypothesis testing using the binomial distribution; includes software and examples.
- [Fitting Pareto Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-pareto-parameters-via-mle/): Describes how to find Pareto distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Order Statistics](https://real-statistics.com/order-statistics/): Tutorial on order statistics for continuous, discrete and finite populations. Describes various properties of order statistics and how to use them in Excel.
- [Distribution of Order Statistics from a Continuous Population](https://real-statistics.com/order-statistics/distribution-order-statistics-continuous-population/): Describes the cdf and pdf of the distribution of order statistics from a continuous population. Includes Excel functions and a variety of examples.
- [Repeated Measures ANOVA Post Hoc Testing](https://real-statistics.com/anova-repeated-measures/repeated-measures-anova-tool/repeated-measures-anova-post-hoc-testing/): Describes how to perform Repeated Measures ANOVA post-hoc tests in Excel using the Real Statistics One Factor Repeated Measures ANOVA data analysis tool.
- [Total Least Squares](https://real-statistics.com/regression/total-least-squares/): Describes how total least squares regression in two variables and how to calculate the linear regression coefficients in Excel. Includes examples and software.
- [Cronbach's Alpha Hypothesis Testing](https://real-statistics.com/reliability/internal-consistency-reliability/cronbachs-alpha/cronbachs-alpha-continued/): Describes how to perform hypothesis testing for Cronbach's Alpha, including confidence intervals. Examples and software in Excel are provided.
- [Correlation - Proofs](https://real-statistics.com/correlation/basic-concepts-correlation/correlation-advanced/): Provides an additional property of correlation and covariance, and includes proofs of properties given in Basic Concepts of Correlation
- [Prim Algorithm (MST)](https://real-statistics.com/other-mathematical-topics/graph-theory/prim-algorithm-mst/): Describes the Prim algorithm for creating a minimum spanning tree (MST) of a connected graph using Excel. Examples and software are included.
- [Monte Carlo Integration](https://real-statistics.com/bayesian-statistics/monte-carlo-integration/): Describes Monte Carlo techniques for calculating integrals, expected values and cumulative distribution functions useful in Bayesian analysis
- [Roots of a Polynomial](https://real-statistics.com/other-mathematical-topics/roots-of-a-polynomial/): Describes how to obtain the complex/real roots of a polynomial in Excel, especially by using Bairstow's method. An Excel function is also provided.
- [Multiple Regression Analysis in Excel](https://real-statistics.com/multiple-regression/multiple-regression-analysis/multiple-regression-analysis-excel/): Describes the multiple regression capabilities provided in standard Excel. Explains the output from Excel's Regression data analysis tool in detail.
- [Studentized Range q Table](https://real-statistics.com/statistics-tables/studentized-range-q-table/): Studentized Range q Table with critical value for q(k, df, α) for α = .10, .025, .05 and .01, .005, .001 and values of k up to 40.
- [Complex Numbers](https://real-statistics.com/other-mathematical-topics/complex-numbers/): Describes how to perform complex number operations in Excel. Examples and software are provided. Includes Excel complex number and Real Statistics formats.
- [Order Statistics from a Discrete Population](https://real-statistics.com/order-statistics/order-statistics-from-a-discrete-population/): Describes the cdf and pdf of the distribution of order statistics from a discrete population. Includes Excel functions and a variety of examples.
- [Dirichlet Distribution](https://real-statistics.com/binomial-and-related-distributions/dirichlet-distribution/): Describes the Dirichlet distribution, a multivariate version of the beta distribution, and how to use it in Excel. Describes the multivariate beta function.
- [Follow-up Tests to Kruskal-Wallis](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/follow-up-tests-kruskal-wallis/): Describes how to perform various follow-up tests after Kruskal-Wallis, including Nemenyi, Dunn's and Dunnett's. Examples and free software are included.
- [Lilliefors Distribution](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/lilliefors-test-normality/lilliefors-distribution/): Describes how to create an estimate of the Lilliefors Distribution, including examples and Excel formulas for calculating values in the distribution.
- [Real Statistics Capabilities for Cox Regression](https://real-statistics.com/survival-analysis/cox-regression/real-statistics-capabilities-for-cox-regression/): Describes the functions and data analysis tools for performing Cox Regression in Excel. Examples and Excel software are included.
- [Holt-Winters Multiplicative Method](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/holt-winters-method/): Tutorial on how to conduct Holt-Winters seasonal forecasting in Excel. Examples & software are provided. Also explains how to use Solver to optimize forecasts.
- [Simple Imputation and Multiple Imputation Constraints](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/multiple-imputation-constraints/): Describes how to use constraints in performing multiple imputation. Excel functions for dealing with this issue are provided as are examples in Excel.
- [Advanced Multiple Correlation](https://real-statistics.com/multiple-regression/multiple-correlation-advanced/): How to use regression to calculate the correlation coefficient in Excel. Includes the partial correlation coefficient and the partial correlation matrix.
- [Power of One Sample Variance Testing](https://real-statistics.com/chi-square-and-f-distributions/power-one-sample-variance-testing/): Describes how to calculate the power of a one sample variance test in Excel and the sample size required for this test. Includes examples and Excel add-in.
- [Noncentral F Distribution](https://real-statistics.com/chi-square-and-f-distributions/noncentral-f-distribution/): Describes how to calculate the noncentral F pdf, distribution and its inverse in Excel. Includes examples and Excel add-in.
- [D'Agostino-Pearson Test](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/dagostino-pearson-test/): Describes the Skewness Test, Kurtosis Test and D'Agostino-Pearson Test for normality and how to calculate them in Excel. Examples and software are provided.
- [Real Statistics Forecasting Tools](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/real-statistics-forecasting-tools/): Explains how to use the Real Statistics data analysis tools to create time-series forecasts in Excel environments. Software and examples are included.
- [Noncentral Chi-square Distribution](https://real-statistics.com/chi-square-and-f-distributions/noncentral-chi-square-distribution/): Describes the noncentral chi-square distribution, including graphs, examples and Excel functions to calculate the distribution and its inverse.
- [Kendall's Tau Normal Approximation](https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-tau-normal-approximation/): Describes how to perform correlation hypothesis testing using Kendall's tau in Excel via normal approximation. Software and examples are provided.
- [Data Analysis Tool for Item Analysis](https://real-statistics.com/reliability/item-analysis/data-analysis-tool-item-analysis/): Describes how to use Real Statistics' Reliability data analysis tool to calculate difficulty and item discrimination index even with partial scores.
- [Measures of Variability Detailed](https://real-statistics.com/descriptive-statistics/measures-variability/measures-variability-detailed/): Proofs of properties about measures of variability, especially variance and standard deviation. Does not require calculus.
- [Pareto Distribution](https://real-statistics.com/other-key-distributions/pareto-distribution/): Describes key properties of the Pareto distribution (pdf, cdf, mean, median, standard deviation, etc.) and how to use this distribution in Excel.
- [Basic Concepts of Matrices](https://real-statistics.com/matrices-and-iterative-procedures/basic-concepts-of-matrices/): Describe some basic properties of a matrix, including square matrix, identity matrix, triangular matrix, vector, scalar, length.
- [Newton's Method](https://real-statistics.com/matrices-and-iterative-procedures/newtons-method/): Describes how to use Newton's method in Excel to find the roots of a non-linear equation and a system of non-linear equations.
- [Order Statistics Proofs](https://real-statistics.com/order-statistics/order-statistics-proofs/): Provides the proofs of various properties related to order statistics. The reader should be aware that these proofs can use calculus.
- [Numerical Differentiation](https://real-statistics.com/other-mathematical-topics/differentiation/): Demonstrates how to perform numerical differentiation in Excel. An Excel function is provided that calculates the derivative for a specified function.
- [Spearman’s Rank Correlation Hypothesis Testing](https://real-statistics.com/correlation/spearmans-rank-correlation/spearmans-rank-correlation-detailed/): Describes how to use Spearman's Rank Correlation for hypothesis testing in Excel to determine whether two samples are independent. Example and software provided
- [Spearman’s Rank Correlation](https://real-statistics.com/correlation/spearmans-rank-correlation/): Provides a description of Spearman’s rank correlation, also called Spearman's rho, and how to calculate it in Excel. This is a non-parametric measure.
- [Kendall’s Tau Basic Concepts](https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-tau-correlation-detailed/): Provides a definition of Kendall's tau correlation and present some of its properties in preparation for describing how to do hypothesis testing.
- [Kendall’s Tau Correlation](https://real-statistics.com/correlation/kendalls-tau-correlation/): Tutorial on Kendall's tau non-parametric correlation coefficient. Including definition, properties, hypothesis testing, examples and Excel software
- [Kendall's Tau Hypothesis Testing](https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-tau-hypothesis-testing/): Describes how to do hypothesis testing for Kendall's tau correlation coefficient for small samples using a table of critical vales. Example is given.
- [Correlation Data Analysis Tool](https://real-statistics.com/correlation/correlation-data-analysis-tool/): Describes how to use the Real Statistics Correlation data analysis tool to calculate Pearson's, Spearman's and Kendall's correlation and do hypothesis testing.
- [Combining Multiple Imputations](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/combining-multiple-imputations/): Detailed description of how to combine multiple imputations in Excel using Little's rules. Includes examples and free add-in software.
- [Autoregressive Process Proofs](https://real-statistics.com/time-series-analysis/autoregressive-processes/autoregressive-processes-basic-concepts/autoregressive-process-proofs/): Provides the proofs of key properties about Autoregressive processes and time series. Proofs use the stationary property.
- [Augmented Dickey-Fuller Test](https://real-statistics.com/time-series-analysis/autoregressive-processes/augmented-dickey-fuller-test/): Describes how to perform the Augmented Dickey-Fuller Test (ADF), which tests whether a time series is stationary, in Excel. Examples and software are included.
- [Matrix Operations Tool](https://real-statistics.com/matrices-and-iterative-procedures/matrix-operations/matrix-operations-tool/): Describes how to use the Real Statistics Matrix Operations data analysis tool. Examples are provided for how to perform these operations in Excel.
- [Kolmogorov Distribution](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/kolmogorov-smirnov-test/kolmogorov-distribution/): Description of the Kolmogorov distribution and how it can be used to calculate the p-value and critical value for the Kolmogorov-Smirnov test; incl. examples.
- [Descriptive Statistics for a Frequency Table](https://real-statistics.com/descriptive-statistics/frequency-tables/descriptive-statistics-frequency-table/): Describes how to calculate descriptive statistics (mean, median, variance, MAD, IQR, etc.) in Excel and by using Real Statistics functions.
- [Conjugate Pairs](https://real-statistics.com/bayesian-statistics/conjugate-pairs/): Illustrates a number of conjugate pairs used in Bayesian analysis (exponential-gamma, Poisson-gamma, etc.). Examples are provided using Excel
- [Advanced Complex Number Operations](https://real-statistics.com/other-mathematical-topics/advanced-complex-number-operations/): Provides some more of the theory about complex numbers used to create the various complex number operations. Emphasis on the power function.
- [Chi-square Distribution - Advanced](https://real-statistics.com/chi-square-and-f-distributions/chi-square-distribution/chi-square-distribution-advanced/): Provides additional technical details about the chi-square distribution and the proofs of properties about the chi-square distribution.
- [Effect Size for Factorial ANOVA](https://real-statistics.com/multiple-regression/effect-size-factorial-anova/): We explore measures of effect size for Factorial ANOVA based on the correlation coefficient (in addition to Cohen's d studied elsewhere).
- [Numerical Integration](https://real-statistics.com/other-mathematical-topics/integration/): Describes various ways of estimating a definite integral, including the midpoint rule, trapezoid rule and Simpson's rule.
- [Numerical Integration Function](https://real-statistics.com/other-mathematical-topics/integration/numerical-integration-function/): Describes how to perform numerical integration for any smooth function in Excel using the Real Statistics INTEGRAL function. Numerous examples are provided.
- [Real Statistics Data Analysis Tools](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/): Lists all the Real Statistics statistical data analysis tools and includes links to get more information about these tools.
- [Binomial Distribution and Random Walks](https://real-statistics.com/binomial-and-related-distributions/binomial-distribution-and-random-walks/): Describes the average dispersion from the mean, which is based on random walks and the binomial distribution. We can obtain an estimate using Excel.
- [Data Analysis for Nested ANOVA](https://real-statistics.com/anova-random-nested-factors/nested-anova/data-analysis-nested-anova/): Describes how to create a nested ANOVA model with one fixed factor and one random factor, esp. using a data analysis tool in the Excel environment
- [Nested ANOVA](https://real-statistics.com/anova-random-nested-factors/nested-anova/): Describes how to create nested ANOVA designs and perform Nested ANOVA in Excel. Includes examples and Excel add-in software.
- [One Random Factor ANOVA](https://real-statistics.com/anova-random-nested-factors/one-random-factor-anova/): Describes how to calculate ANOVA for one random factor in Excel, including estimates of the population mean and between group and error variances.
- [PLS Regression Bootstrapping](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/partial-least-squares-pls-regression/pls-regression-bootstrapping/): Describes Excel worksheet functions in the Real Statistics Resource Pack to support bootstrapping for PLS regression models. Examples are provided.
- [Bootstrapping Multivariate Regression Support](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-bootstrapping/bootstrapping-multivariate-regression-support/): Describes Excel worksheet functions in the Real Statistics Resource Pack to support bootstrapping for multivariate regression models. Examples are provided.
- [Multivariate Regression Bootstrapping](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-bootstrapping/): How to use bootstrapping in multivariate regression modelling to estimate standard errors & confidence/prediction intervals. Provides Excel examples & software
- [Bootstrapping Regression Support](https://real-statistics.com/multiple-regression/bootstrapping-regression/bootstrapping-regression-support/): Describes Excel worksheet functions provided by the Real Statistics Resource Pack in support of bootstrapping for regression models. Examples are also provided.
- [Bootstrapping Regression Models](https://real-statistics.com/multiple-regression/bootstrapping-regression/): Describes how to use bootstrapping in regression modelling to estimate standard errors and confidence/prediction intervals. Provides Excel examples and software
- [Hotelling's T-square Effect Size](https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/one-sample-hotellings-t-square/hotellings-t-square-effect-size/): Describes two measures of effect size for the one-sample Hotelling's T-square test: partial eta-square and Mahalanobis distance squared.
- [ANCOVA when slopes assumption is not met](https://real-statistics.com/analysis-of-covariance-ancova/ancova-slopes-assumption-not-met/): Describes how to perform an ANCOVA-like analysis in Excel even when the homogeneity of slopes assumption is violated, Includes examples and analysis tool.
- [ANCOVA Light Basic Concepts](https://real-statistics.com/analysis-of-covariance-ancova/ancova-slopes-assumption-not-met/ancova-light-basic-concepts/): Describes an ANCOVA-like test using regression even when the homogeneity of slopes assumption is violated. We show how this is done in Excel.
- [ANCOVA Light: Real Statistics Support](https://real-statistics.com/analysis-of-covariance-ancova/ancova-slopes-assumption-not-met/ancova-light-tool/): Describes how to use an ANCOVA-like test in Excel using regression even when the homogeneity of slopes assumption is violated.
- [Contact Us](https://real-statistics.com/contact-us/): Provides key contact information: author's email address and a link to the author's profile. Comments from the user community is welcomed.
- [Best fit model for three-way contingency tables](https://real-statistics.com/log-linear-regression/three-way-contingency-tables/best-fit-model-three-way-contingency-tables/): How to determine in Excel which log-linear regression model is the best fit for data represented in a three-way contingency table. Also find model coefficients.
- [ANOVA approach to ANCOVA](https://real-statistics.com/analysis-of-covariance-ancova/anova-approach-ancova/): How to perform analysis of covariance (ANCOVA) in Excel using ANOVA tools built into Excel. Examples and special software provided.
- [Cohen's Kappa](https://real-statistics.com/reliability/interrater-reliability/cohens-kappa/): Tutorial on how to calculate and use Cohen's kappa, a measure of the degree of consistency between two raters. Examples are provided using Excel.
- [Comparing the slopes for two independent samples](https://real-statistics.com/regression/hypothesis-testing-significance-regression-line-slope/comparing-slopes-two-independent-samples/): Using Excel to perform hypothesis testing to determine whether the regression lines which model two independent samples have the same slope.
- [Root-finding Functions](https://real-statistics.com/other-mathematical-topics/roots-of-a-continuous-function/root-finding-functions/): Describes how to use the bisection, secant, Newton's and Brent's approaches to finding roots of a function in Excel via Real Statistics.
- [Maximum/minimum values of a continuous function](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/): Describes how to identify local and global maximum and minimum values of a function using Newton's method. Excel worksheet functions are described.
- [Matrix Operations](https://real-statistics.com/matrices-and-iterative-procedures/matrix-operations/): Describes how to use various matrix operations (e.g. multiplication, addition, inverse, transpose, QR decomposition, eigenvalues and vectors, etc.) in Excel.
- [Local maxima/minima of a multivariate function](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/local-maxima-minima-multivariate/): Describes how to identify local maximum and minimum values of a function f(x,y) or f(x,y,z) using Newton's method. Includes Excel worksheet functions.
- [Frechet Distribution](https://real-statistics.com/other-key-distributions/frechet-distribution/): Describes key properties of the Frechet distribution (pdf, cdf, mean, median, standard deviation, etc.) and how to use this distribution in Excel.
- [Double MAD](https://real-statistics.com/descriptive-statistics/mad-and-outliers/double-mad/): Describes the Double MAD statistic and how it is used to identify outliers. Describes an Excel function that implements the Double MAD. Includes examples.
- [Identifying Outliers using Harrell-Davis Median](https://real-statistics.com/descriptive-statistics/mad-and-outliers/identifying-outliers-using-harrell-davis-median/): Describes how to use the Harrell-Davis median and the related MAD and Double MAD measures to identify outliers. Includes an example in Excel.
- [Generalized Extreme Value Distribution](https://real-statistics.com/other-key-distributions/generalized-extreme-value-distribution/): Describes the Generalized Extreme Value (GEV) distribution and how to use it in Excel, esp. for determining the risk of extreme events.
- [Fitting GEV Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-gev-distribution-mle/): Describes how to find GEV distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Method of Moments: GEV Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-gev-distribution/): Describes how to estimate the mu, sigma and xi parameters of the GEV distribution that best fits a set of data using the method of moments in Excel.
- [Other measures of effect size for ANOVA](https://real-statistics.com/multiple-regression/other-measures-effect-size-anova/): We explore measures of effect size for One-way ANOVA based on the correlation coefficient (in addition to Cohen's d studied elsewhere).
- [McNemar’s Test](https://real-statistics.com/non-parametric-tests/mcnemars-test/): Describes how to perform McNemar's non-parametric test. Excel examples are provided as are worksheet functions to implement the test in Excel.
- [Additional information about sphericity](https://real-statistics.com/anova-repeated-measures/sphericity/additional-information-sphericity/): How to calculate in Excel the Greenhouse-Geisser epsilon, esp. using eigenvalues, as well as the Mauchly and John, Nagao and Sugiura's tests for sphericity.
- [Return Period and Return Level](https://real-statistics.com/other-key-distributions/generalized-extreme-value-distribution/return-period-and-return-level/): Defines the concepts of return period and return level and provides an example in Excel to calculate the return level for flood control.
- [Confidence Interval for Coefficient of Variation](https://real-statistics.com/students-t-distribution/confidence-interval-coefficient-of-variation/): Describes how to calculate a confidence interval for the coefficient of variation in Excel using the Kelley, Naive, McKay and Vangel approaches.
- [Two within-subjects factors structural model](https://real-statistics.com/anova-repeated-measures/two-within-subjects-factors/two-within-subjects-factors-structural-model/): Describes the structural model for ANOVA with repeated measures with two within-subjects factors. Provides the theory for this type of repeated-measures ANOVA.
- [Correlation in Relationship to t-test](https://real-statistics.com/correlation/dichotomous-variables-t-test/): Correlation of dichotomous variables and relation to t-test. In this way two sample comparison of means t-testing can be turned into a correlation problem.
- [Kendall's Correlation Testing using a Fisher Transformation](https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-correlation-testing-using-a-fisher-transformation/): How to test in Excel whether a population's Kendall's tau is significantly different from some value using a Fisher transformation. Incl. example and software.
- [Kendall's Correlation Testing with Ties](https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-correlation-testing-with-ties/): Describes how to perform hypothesis testin for Kendall's tau correlation coefficient when there are a large number of ties.
- [Homogeneous association model](https://real-statistics.com/log-linear-regression/three-way-contingency-tables/homogeneous-association-model/): How to determine in Excel how good a fit a homogeneous association log-linear regression model is for data represented in a three-way contingency table.
- [Basic Concepts of Correlation](https://real-statistics.com/correlation/basic-concepts-correlation/): Defines correlation and covariance and provides their basic properties and how to compute them in Excel. Includes data in frequency tables.
- [Paired Sample t-Test](https://real-statistics.com/students-t-distribution/paired-sample-t-test/): Describes how to use the t-test in Excel to determine whether two paired samples have equal means. We provide examples using standard Excel and Real Statistics.
- [Chi-square Test for Normality](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/chi-square-test-for-normality/): How to use the chi-square goodness of fit test to determine in Excel whether sample data comes from a population which is normally distributed.
- [Residuals](https://real-statistics.com/multiple-regression/residuals/): Describes how to calculate and plot residuals in Excel. Raw residuals, standardized residuals and studentized residuals are included.
- [Joint and Range Distribution from a Discrete Population](https://real-statistics.com/order-statistics/joint-and-range-distribution-from-a-discrete-population/): Describes the joint and range distribution of order statistics from a discrete population. Includes Excel functions and a variety of examples.
- [Order Statistics for a Uniform Population](https://real-statistics.com/order-statistics/order-statistics-uniform-population/): Describes order statistics from a uniform population and generalizations to all populations. Includes properties and provides a number of examples using Excel.
- [Joint and Range Distribution from a Continuous Population](https://real-statistics.com/order-statistics/joint-and-range-distribution-from-a-continuous-population/): Describes the joint and range distribution of order statistics from a continuous population. Includes Excel functions and a variety of examples.
- [Bootstrapping for Order Statistics](https://real-statistics.com/order-statistics/confidence-intervals-order-statistics/bootstrapping-for-order-statistics/): Describes how to use bootstrapping in Excel to estimate the confidence interval of order statistics, the median and percentiles.
- [Simulation for Order Statistics](https://real-statistics.com/order-statistics/confidence-intervals-order-statistics/simulation-order-statistics/): Describes how to conduct Monte Carlo simulation in Excel to estimate the confidence interval of order statistics, the median and percentiles
- [Sample Median Theorem](https://real-statistics.com/order-statistics/confidence-intervals-order-statistics/sample-median-theorem/): Describes the Sample Median Theorem, the median equivalent to the Central Limit Theorem. Implements the theorem in Excel and provides examples of its use.
- [Global maximum/minimum of a multivariate function](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/global-maximum-minimum-multivariate/): Describes how to identify global maximum and minimum values of a function f(x,y) or f(x,y,z) using Newton's method. Includes Excel worksheet functions.
- [Roots of a Continuous Function](https://real-statistics.com/other-mathematical-topics/roots-of-a-continuous-function/): Describes how to calculate the roots of a continuous function. Includes Brent's, Newton's, Bisection and Secant methods. Includes description of Excel functions
- [Roots of Multivariate Functions](https://real-statistics.com/other-mathematical-topics/roots-of-a-continuous-function/multidimensional-roots/): Describes how to find roots of two functions in two unknowns or three functions in three unknowns in Excel using Newton's method, incl Excel worksheet functions
- [Inflection Point](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/inflection-point/): Provides a definition of an inflection point and demonstrates how to find an inflection point in Excel using the fact that the second derivative is zero.
- [One-Sample t-Test](https://real-statistics.com/students-t-distribution/one-sample-t-test/): Describes the one-sample t-test and how to carry it out in Excel. Includes assumptions, confidence intervals, power, and sample size requirements.
- [Harrell-Davis Quantiles](https://real-statistics.com/descriptive-statistics/ranking-function-excel/harrell-davis-quantiles/): Describes the Harrell-Davis Quantile and its advantage over the usual quantile/percentile measures. Includes Excel worksheet function.
- [Extreme Value Applications and Theory](https://real-statistics.com/other-key-distributions/generalized-extreme-value-distribution/extreme-value-applications-theory/): Describes how the Generalized Extreme Value (GEV) distribution is used to predict extreme events. Also, some properties of the GEV distribution are explained.
- [Detailed Within-Subjects Analysis](https://real-statistics.com/anova-repeated-measures/one-between-subjects-factor-and-one-within-subjects-factor/detailed-within-subjects-analysis/): Describes a more detailed within-subjects analysis in Excel for ANOVA repeated measures with one within-subjects factor and one between-subjects factor.
- [Descriptive Statistics and Normality Tool](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/descriptive-statistics-normality-tool/): Describes in detail Real Statistics' Descriptive Statistics and Normality data analysis tool. Provides descriptive statistics and normality testing in Excel.
- [Resampling Procedures](https://real-statistics.com/non-parametric-tests/resampling-procedures/): How to perform resampling tests, especially as non-parametric versions of the t-tests for independent samples and paired samples.
- [Scatter Diagrams](https://real-statistics.com/correlation/scatter-diagrams/): Describes scatter diagrams as a method for illustrating the correlation between two variables, and shows how to produce a scatter diagram as a chart in Excel.
- [Correlation and Chi-square Test for Independence](https://real-statistics.com/correlation/dichotomous-variables-chi-square-independence-testing/): How to perform a correlation test on dichotomous variables to get the same results as can be obtained by using the chi-square test for independence.
- [Polynomial Regression](https://real-statistics.com/multiple-regression/polynomial-regression/): Describes how to use the multiple regression model to investigate whether data fits a polynomial model. Examples using Excel are provided.
- [t Distribution Basic Concepts](https://real-statistics.com/students-t-distribution/t-distribution-basic-concepts/): Describes the basic properties of the Student's t distribution, its relationship to sampling and the Central Limit Theorem as well as key Excel formulas.
- [Neural Network Excel Example](https://real-statistics.com/neural-networks/neural-network-excel-example/): Describes how to use the Real Statistics training and testing data analysis tools to build a neural network that performs simple addition in Excel.
- [Distribution of order statistics from finite population](https://real-statistics.com/other-key-distributions/uniform-distribution/order-statistics-finite-population/): Describes order statistics from a finite population and how they are distributed. Various Excel worksheet functions are defined and examples are included.
- [Two-way Repeated Measures Anova Tool](https://real-statistics.com/anova-repeated-measures/two-within-subjects-factors/two-way-repeated-measures-anova-tool/): Describes in detail how to perform ANOVA repeated measures with two within-subjects factors. Describes Real Statistics data analysis tool.
- [Outliers and Influencers](https://real-statistics.com/multiple-regression/outliers-and-influencers/): How to identify outliers anf influencers for multiple regression models in Excel, including the concepts of Cook's distance, DFFITS and studentized residuals.
- [Transformations to Create Symmetry](https://real-statistics.com/tests-normality-and-symmetry/transformations-symmetry/): Explains how to use transformations, especially log transformations, to make data more symmetric. An Excel example is provided to illustrate.
- [Graphical Tests for Normality and Symmetry](https://real-statistics.com/tests-normality-and-symmetry/graphical-tests-normality-symmetry/): Describes how to use graphs (histogram, QQ plot and box plot) to determine whether data are normally distributed and/or symmetric. Excel examples are provided.
- [Sign Test](https://real-statistics.com/non-parametric-tests/sign-test/): Describe how to perform the sign test in Excel. Also describes the supplemental Real Statistics function to perform the sign test.
- [Surface Chart](https://real-statistics.com/other-mathematical-topics/surface-chart/): Describes how to construct a surface chart in Excel and how to plot a function in two variables using Excel-s Surface Chart and Real Statistics capabilities.
- [Real Statistics Support for Wordle](https://real-statistics.com/wordle-strategy/real-statistics-wordle-support/): Describes how to determine the best three guesses for winning at Wordle in Excel using Real Statistics worksheet functions.
- [Wordle Letter Frequency and Patterns](https://real-statistics.com/wordle-strategy/wordle-letter-frequency-and-patterns/): Presents one approach for making your initial guess in Wordle based on using words with letters that occur most frequently in the Wordle dictionary.
- [Winning Wordle in Two Tries](https://real-statistics.com/wordle-strategy/winning-wordle-in-two-tries/): Describes the strategy for winning Wordle in one or two guesses by finding the words that have the most non-zero patterns.
- [Best First Two Guesses in Wordle](https://real-statistics.com/wordle-strategy/best-first-two-guesses-wordle/): Describes how to make your best first and second guesses in Wordle by finding the word that has the most non-zero patterns.
- [Weibull Distribution](https://real-statistics.com/other-key-distributions/weibull-distribution/): Describes the use of the Weibull distribution to calculate the mean time to failure (MTTF) and mean time between failures (MTBF) using Excel. Includes example.
- [Effect Size for Chi-square Test](https://real-statistics.com/chi-square-and-f-distributions/effect-size-chi-square/): Describes three effect size measures for chi-square test of independence: phi, Cramer's V and odds ratio. Describes how to calculate them in Excel.
- [Goodness of Fit](https://real-statistics.com/chi-square-and-f-distributions/goodness-of-fit/): How to test for goodness of fit using Excel (chi-square). These tests can also be used to check whether observed data fit a certain pattern or distribution.
- [Independence Testing](https://real-statistics.com/chi-square-and-f-distributions/independence-testing/): How to test in Excel whether two categorical random variables are independent. Data is organized in a contingency table and tested using a chi-square test.
- [ANOVA Follow-up Analyses](https://real-statistics.com/two-way-anova/anova-follow-up-analyses/): Describes how to perform follow-up analyses to ANOVA in Excel. Approach is esp. applicable to Three Factor ANOVA. Incl. contrasts and Tukey HSD. Examples given.
- [Three Factor ANOVA without Replication](https://real-statistics.com/two-way-anova/three-factor-anova-without-replication/): Describes how to perform three-factor ANOVA without replication in Excel. Example and software are provided. Includes the Real Statistics data analysis tool.
- [Real Statistics Support for Three Factor ANOVA](https://real-statistics.com/two-way-anova/real-statistics-support-three-factor-anova/): Describes the various Three Factor ANOVA supplemental functions and data analysis tools provided in the Real Statistics software, which is an Excel add-in.
- [ANOVA with more than Two Factors](https://real-statistics.com/two-way-anova/anova-more-than-two-factors/): How to carry out ANOVA with replication for three factors in Excel. Defines various versions of MS, SS and df and how to formula the appropriate tests.
- [Mann-Whitney Table](https://real-statistics.com/statistics-tables/mann-whitney-table/): Mann-Whitney Table for independent samples for values of alpha = .01, .02, .05, .10 (two-tailed). This table contains the critical values for MW test.
- [Eigenvectors for Non-Symmetric Matrices](https://real-statistics.com/linear-algebra-matrix-topics/eigenvectors-for-non-symmetric-matrices/): Describes how to use Schur's decomposition to find all the real eigenvalues and eigenvectors in Excel even for non-symmetric matrices.
- [Linear Algebra Background for Factor Analysis](https://real-statistics.com/multivariate-statistics/factor-analysis/linear-algebra-background-factor-analysis/): Summary of the key facts from linear algebra that are necessary to perform factor analysis, esp. the Spectral Decomposition Theorem.
- [Matrices and Iterative Procedures](https://real-statistics.com/matrices-and-iterative-procedures/): Key characteristics and operations on matrices in Excel and iterative methods: Newton's method, Goal Seek and Iterative Proportional Fitting Procedure (IPFP).
- [Linear Independent Vectors](https://real-statistics.com/linear-algebra-matrix-topics/linear-independent-vectors/): Describes fundamental properties of linear independence and the basis of a set of vectors. Describes concepts such as span and dimension as well.
- [Linear Algebra and Advanced Matrix Topics](https://real-statistics.com/linear-algebra-matrix-topics/): Tutorial on linear algebra and advanced matrix topics required for a good foundation for the study of multivariate statistics.
- [Complex eigenvalues and eigenvectors continued](https://real-statistics.com/linear-algebra-matrix-topics/eigenvalues-eigenvectors/complex-eigenvectors-continued/): Describes how to obtain complex eigenvectors from a real matrix in Excel complex number format. Also provides info about eigenvectors of repeated eigenvalues.
- [Complex eigenvalues and eigenvectors](https://real-statistics.com/linear-algebra-matrix-topics/eigenvalues-eigenvectors/complex-eigenvalues-and-eigenvectors/): Describes how to obtain both the real and complex eigenvalues and eigenvectors from a real-valued square matrix using Real Statistics function in Excel.
- [Eigenvectors for repeated eigenvalues](https://real-statistics.com/linear-algebra-matrix-topics/eigenvalues-eigenvectors/eigenvectors-for-repeated-eigenvalues/): Describes how to identify distinct eigenvectors corresponding to eigenvalues with multiplicity greater than 1. Includes Excel examples and worksheet function.
- [Eigenvalue and eigenvector functions](https://real-statistics.com/linear-algebra-matrix-topics/eigenvalues-eigenvectors/eigenvalue-and-eigenvector-functions/): Describes the Real Statistics worksheet functions that calculate the eigenvalues and eigenvectors of a square matrix in Excel.
- [Discriminant Analysis Tools](https://real-statistics.com/multivariate-statistics/discriminant-analysis/discriminant-analysis-tools/): Describes the Real Statistics discriminant analysis data analysis tool and functions. Examples are provided for both LDA and QDA.
- [LAMBDA-based Functions](https://real-statistics.com/excel-environment/lambda-functions/lambda-based-functions/): Describes how to use the following LAMBDA-based worksheet functions in Excel: BYROW, BYCOL, REDUCE, MAP, SCAN and MAKEARRAY.
- [System of Linear Equations](https://real-statistics.com/matrices-and-iterative-procedures/system-linear-equations/): Describes how to solve systems of m linear equations in n unknowns in Excel. Explores Gaussian elimination, determinants and matrix inversion approaches.
- [QR Factorization Continued](https://real-statistics.com/linear-algebra-matrix-topics/qr-factorization/qr-factorization-continued/): Describes QR factorization (reduced and full) where the number of rows in the matrix is less than the number of columns. Examples are provided.
- [Varimax Algorithm](https://real-statistics.com/linear-algebra-matrix-topics/varimax/): Shows how to perform the iterative algorithm for Varimax rotation, step by step, in Excel. Includes an example where all the steps are explained.
- [Rank of a Matrix](https://real-statistics.com/linear-algebra-matrix-topics/matrix-rank/): Review of rank of a matrix and its relationship to solutions to linear equations (and Gaussian elimination), dimension, null space and range.
- [Spectral Decomposition](https://real-statistics.com/linear-algebra-matrix-topics/spectral-decomposition/): Tutorial on spectral decomposition theorem and the concepts of algebraic multiplicity. Includes its relationship to eigenvalues and eigenvectors.
- [Singular Value Decomposition](https://real-statistics.com/linear-algebra-matrix-topics/singular-value-decomposition/): Tutorial on the Singular Value Decomposition and how to calculate it in Excel. Also describes the pseudo-inverse of a matrix and how to calculate it in Excel.
- [Schur's Factorization](https://real-statistics.com/linear-algebra-matrix-topics/schur-factorization/): Describes how to find the Schur's decomposition for a square matrix, which will be used to calculate real eigenvectors for non-symmetric matrices in Excel
- [Cholesky Decomposition](https://real-statistics.com/linear-algebra-matrix-topics/cholesky-decomposition/): Tutorial on the Cholesky Decomposition and how to calculate it in Excel. Also provides an example and free software add-in.
- [QR Factorization](https://real-statistics.com/linear-algebra-matrix-topics/qr-factorization/): Tutorial on QR Factorization (also called QR Decomposition) and how to carry it out in Excel. Includes discussion of the Householder process.
- [Positive Definite Matrices](https://real-statistics.com/linear-algebra-matrix-topics/positive-definite-matrices/): Tutorial on positive definite and semidefinite matrices and how to calculate the square root of a matrix in Excel. Provides theory and examples.
- [Symmetric Matrices](https://real-statistics.com/linear-algebra-matrix-topics/symmetric-matrices/): Description of key facts about symmetric matrices: especially the spectral decomposition theorem and orthogonal diagonalization.
- [Orthogonal Vectors and Matrices](https://real-statistics.com/linear-algebra-matrix-topics/orthogonal-vectors-matrices/): Tutorial on orthogonal vectors and matrices, including the Gram-Schmidt Process for constructing an orthonormal basis. Also Gram Schmidt calculator in Excel.
- [Eigenvalues and Eigenvectors](https://real-statistics.com/linear-algebra-matrix-topics/eigenvalues-eigenvectors/): Tutorial on eigenvalues and eigenvectors, plus access to functions that calculate the eigenvalues and eigenvectors of a square matrix in Excel.
- [Hessenberg Decomposition](https://real-statistics.com/linear-algebra-matrix-topics/hessenberg-decomposition/): Describes how to identify a Hessenberg decomposition of a square matrix in Excel based on an upper triangular matrix, tridiagonal matrix for a symmetric matrix.
- [Pseudo-inverse](https://real-statistics.com/linear-algebra-matrix-topics/pseudo-inverse/): Describes how to find the pseudo-inverse of a matrix in Excel for matrices of full rank or not of full rank. Example examples and functions provided.
- [Confidence Interval for Ratio of Variances](https://real-statistics.com/chi-square-and-f-distributions/confidence-interval-variance-ratio/): Describe how to create a confidence interval for two-sample variance testing using an Ftest in Excel. Examples are provided.
- [Chi-square Distribution](https://real-statistics.com/chi-square-and-f-distributions/chi-square-distribution/): Describe the basic properties of the chi-square distribution, especially its relationship to the normal distribution) and explain supporting Excel formulas.
- [Fitting 3-Parameter Weibull Distribution using MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-3-parameter-weibull-distribution-using-mle/): Describes how to fit a 3 parameter Weibull distribution to a data set using maximum likelihood estimation (MLE). We show how this is done in Excel.
- [Method of Moments: 3 Parameter Weibull Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-weibull/method-of-moments-3-parameter-weibull-distribution/): Describes how to estimate the parameter of the 3 parameter Weibull distribution that fits a set of data using the method of moments in Excel.
- [Three-parameter Weibull Distribution](https://real-statistics.com/other-key-distributions/weibull-distribution/three-parameter-weibull-distribution/): Describes the key characteristics (mean, mode, pdf, cdf, etc.) of the three-parameter Weibull distribution and how to use this distribution in Excel.
- [Bayesian Approach for Two Binomial Samples](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/): Describes how to apply various Bayesian techniques (grid, MCMC, beta conjugate prior) to two samples whose data follows a binomial distribution. Excel examples.
- [Real Statistics Bayesian Analysis Functions](https://real-statistics.com/real-statistics-environment/real-statistics-bayesian-analysis-functions/): Briefly describes all the Real Statistics worksheet functions related to Bayesian statistical analysis and provides links for more information about each one
- [Two Sample Binomial Grid](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/two-sample-binomial-grid/): Describes how to estimate the posterior distribution for two samples that are binomially distributed using a grid in Excel.
- [Two Binomial Samples Beta Prior](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/two-binomial-samples-beta-prior/): Describes how to determine the posterior distribution for two samples that are binomially distributed assuming a beta prior in Excel.
- [Markov-Chain Monte Carlo](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/markov-chain-monte-carlo/): Introduction to Markov-Chain Monte Carlo (MCMC) for data that follows a binomial distribution. An example of a Markov chain is presented.
- [Analytic Approach for Binomial Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/): Describes how to calculate the posterior pdf for binomially distributed data with a beta prior, as well as the HDI. Includes Excel examples and software.
- [Two Sample t Test: equal variances](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/two-sample-t-test-equal-variances/): How to test whether two independent samples, with equal variances, have equal means. Describes Cohen's effect size and Hedges' unbiased effect size.
- [Two Sample t Test: unequal variances](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/two-sample-t-test-uequal-variances/): How to use the t test in Excel to determine whether two independent samples have equal means where the variances are unknown and unequal.
- [Shapiro-Wilk Original Test](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/shapiro-wilk-test/): Describes how to perform the original Shapiro-Wilk test for normality in Excel. Detailed examples are also provided to illustrate the steps.
- [Shapiro-Wilk Expanded Test](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/shapiro-wilk-expanded-test/): Describes how to perform the Shapiro-Wilk test for samples with up to 5,000 elements (Royston version) in Excel. Detailed examples are provided.
- [Kolmogorov-Smirnov Test for Normality](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/kolmogorov-smirnov-test/): Describes how to perform a step-by-step implementation of the Kolmogorov-Smirnov Test in Excel to determine whether sample data is normally distributed.
- [Dunnett's Table](https://real-statistics.com/statistics-tables/dunnetts-table/): Provides the table of critical values for Dunnett's test (two-tailed test). This test is used for comparisons with a control (post-hoc test after ANOVA).
- [Durbin-Watson Table](https://real-statistics.com/statistics-tables/durbin-watson-table/): Durbin-Watson Table of critical values (lower and upper bounds) for values of alpha = .01 and .05. This table is used to test for autocorrelation.
- [Spearman’s Rho Table](https://real-statistics.com/statistics-tables/spearmans-rho-table/): Provides a table of critical values for the Spearman’s Rho Test for significance levels alpha = .01, .02, .05, .10 and sample size up to 30.
- [Statistical Power of the t tests](https://real-statistics.com/students-t-distribution/statistical-power-of-the-t-tests/): Describes how to use the noncentral t distribution to compute the power of t tests. Examples and Excel add-in software are provided.
- [Power of the One-Sample t-Test](https://real-statistics.com/students-t-distribution/one-sample-t-test/power-one-sample-t-test/): Describes how to calculate the statistical power of a one-sample t-test using Excel's Goal Seek capability. Also shows how to estimate the required sample size.
- [Uniform Distribution](https://real-statistics.com/other-key-distributions/uniform-distribution/): Provides a brief overview of the continuous uniform distribution, including key properties and examples using Excel. Includes links to related webpages.
- [Ranking Functions in Excel](https://real-statistics.com/descriptive-statistics/ranking-function-excel/): Describes how to calculate the ranking, percentile, percent rank, and quartile functions in Excel via RANK.AVG, PERCENTILE.EXC, QUARTILE.EXC, etc.
- [Basic Characteristics of the Normal Distribution](https://real-statistics.com/normal-distribution/basic-characteristics-normal-distribution/): Describes the normal distribution and a number of key properties as well as how to calculate and use its pdf and cdf in Excel.
- [Outliers and Robustness](https://real-statistics.com/descriptive-statistics/outliers-and-robustness/): How to identify outliers in Excel and create more robust data in Excel, especially via TRIMMEAN and Winsorized samples. Includes examples and free software.
- [Statistical Power and Sample Size](https://real-statistics.com/sampling-distributions/statistical-power-sample/): How to use Excel's Goal Seek to determine the statistical power of a sample or determine how big a sample is needed to obtain a given power. Includes examples.
- [Binomial Distribution](https://real-statistics.com/binomial-and-related-distributions/binomial-distribution/): Describes the main properties of the binomial distribution and how to use it to perform statistical analyses in Excel. Examples are provided.
- [Exponential Distribution](https://real-statistics.com/other-key-distributions/exponential-distribution/): Brief description of the exponential distribution, which describes the inter-arrival times in a Poisson process and is useful in statistics.
- [Hypergeometric Distribution](https://real-statistics.com/binomial-and-related-distributions/hypergeometric-distribution/): How to use the hypergeometric distribution in Excel to solve problems similar to those using the binomial distribution but with sampling without replacement.
- [Beta Distribution](https://real-statistics.com/binomial-and-related-distributions/beta-distribution/): How to find the probability of success on any single trial in Excel for a specific sample size and total number of successes using the beta distribution.
- [Negative Binomial and Geometric Distributions](https://real-statistics.com/binomial-and-related-distributions/negative-binomial-and-geometric-distributions/): How to use the negative binomial and geometric distributions to solve problems related to the binomial distribution in Excel.
- [TLS Regression Confidence Interval](https://real-statistics.com/regression/total-least-squares/tls-regression-confidence-interval/): Describes how to estimate the standard errors and confidence intervals for TLS regression coefficients in Excel. Incl. example of comparison with gold standard.
- [Wordle Winning Strategy](https://real-statistics.com/wordle-strategy/): Presents the rules of Wordle, provides a list of the 2,315 words in the dictionary and begins a tutorial on the strategy for winning the game.
- [Appendix](https://real-statistics.com/appendix/): The Appendix provides useful background information as well as some summaries of features covered elsewhere in the website.
- [Standard Error for Krippendorff's Alpha](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/standard-error-for-krippendorffs-alpha/): Describes how to calculate the standard error and confidence intervals for Krippendorff's alpha in Excel. Includes an example to demonstrate the steps.
- [Real Statistics Support for Krippendorff's Alpha](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/real-statistics-support-krippendorffs-alpha/): Describes Real Statistics support (Excel worksheet functions and data analysis tools) for Krippendorff's Alpha. Examples are given.
- [Gwet's AC2 Analysis Tools](https://real-statistics.com/reliability/interrater-reliability/gwets-ac2/gwets-ac2-analysis-tool/): Describes Excel worksheet functions and data analysis tools to calculate Gwet's AC2 and its confidence intervals. An example is given.
- [Gwet's AC2 Confidence Interval](https://real-statistics.com/reliability/interrater-reliability/gwets-ac2/gwets-ac2-confidence-interval/): Describes how to calculate the standard error and confidence intervals for Gwet's AC2 interrater reliability statistic in Excel. An example is given.
- [Gwet's AC2 Basic Concepts](https://real-statistics.com/reliability/interrater-reliability/gwets-ac2/gwets-ac2-basic-concepts/): Describes how to calculate Gwet's AC2 (and AC1) interrater reliability statistic in Excel. Excel examples and software are provided
- [Gwet's AC1 and AC2](https://real-statistics.com/reliability/interrater-reliability/gwets-ac2/): Tutorial on Gwet's AC2 (or AC1), including basic concepts, how to calculate alpha and its confidence interval in Excel. Examples and software are provided.
- [Krippendorff's Alpha Basic Concepts](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/krippendorffs-alpha-basic-concepts/): Provides an overview of Krippendorff's Alpha, a measure of interrater reliability, and how to calculate it in Excel. Examples are provided.
- [Krippendorff's Alpha](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/): Tutorial on Krippendorff's Alpha, including basic concepts, how to calculate alpha and its confidence interval in Excel. Examples and software are provided
- [Non-Categorical Ratings for Krippendorff's Alpha](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/non-categorical-ratings-krippendorffs-alpha/): Describes how to calculate Krippendorff's alpha, a measure of interrater reliability, in Excel for interval, ordinal, or ratio ratings. Examples are provided.
- [Simulation Chi-square Test](https://real-statistics.com/chi-square-and-f-distributions/simulation-chi-square-test/): Describes how to calculate a quasi-exact version of the chi-square test for independence using simulation in Excel. Examples and software are provided
- [ZIP Data Analysis Options](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/zip-data-analysis-options/): Describes how to use the (1) Use of the Init Coeff Range field and (2) LL0 options of Real Statistics' ZIP Regression data analysis tool.
- [Zero-Inflated Poisson (ZIP) Regression Predictions](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/zero-inflated-poisson-zip-regression-predictions/): Describes how to use a Zero-Inflated Poisson (ZIP) Regression model to make predictions about count data in Excel using Real Statistics resources.
- [Vuong's Test](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/vuongs-test/): How to use Vuong's test to determine whether the results from ZIP regression are significantly different from ordinary Poisson regression. Incl. Excel example.
- [Constructing a Zero-Inflated Poisson Regression Model](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/constructing-a-zero-inflated-poisson-regression-model/): We show how to construct a Zero-Inflated Poisson (ZIP) Regression model in Excel using a Real Statistics data analysis tool, which in turn uses Solver.
- [ZTP Regression Predictions](https://real-statistics.com/poisson-regression/zero-truncated-poisson-regression/ztp-predictions/): How to use the Excel worksheet functions provided by the Real Statistics Resource Pack to make predictions based on Zero-Truncated Poisson (ZTP) regression.
- [Creating a ZTP Regression model using Solver](https://real-statistics.com/poisson-regression/zero-truncated-poisson-regression/creating-a-ztp-regression-model-using-solver/): Describes how to use the Real Statistics Poisson Regression data analysis tool to perform Zero-Truncated Poisson (ZTP) regression in Excel.
- [Zero-Inflated Poisson Regression](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/): Describes how to perform zero-inflated Poisson (ZIP) regression in Excel. Includes examples and Excel-based data analysis support and worksheet functions.
- [Zero-Truncated Poisson Regression](https://real-statistics.com/poisson-regression/zero-truncated-poisson-regression/): Describes how to perform zero-truncated Poisson (ZTP) regression in Excel. Includes examples and Excel-based data analysis support and worksheet functions.
- [Poisson Regression Over-dispersion Tests](https://real-statistics.com/poisson-regression/poisson-regression-over-dispersion-tests/): Describes how to test for over-dispersion in Poisson regression. Shows how to perform the Score test and Lagrange Multiplier tests. Includes Excel example.
- [ROC Curve and Classification Table](https://real-statistics.com/descriptive-statistics/roc-curve-classification-table/): Describes how to construct a ROC curve and classification table (aka a comfusion matrix) in Excel. Software and examples are given.
- [Classification Table](https://real-statistics.com/descriptive-statistics/roc-curve-classification-table/classification-table/): Describes how to construct a classification table (aka a confusion matrix) in Excel with observed and predicted positive/negative values, TPR, NPR, etc.
- [Runs Distribution](https://real-statistics.com/non-parametric-tests/one-sample-runs-test/runs-distribution/): Describes the run distribution, how to calculate it and its inverse in Excel and how to use it to get an exact value for the runs test. Software and examples.
- [Frequency Table Tool](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/frequency-table-tool/): Describes in detail Real Statistics' Frequency Table data analysis tool. Provides descriptive statistics and normality testing in Excel.
- [Exponential Distribution Examples](https://real-statistics.com/other-key-distributions/exponential-distribution/exponential-distribution-examples/): Presents examples in Excel that use the exponential distribution. Includes interarrival time, MTTF, and product reliability acceptance test.
- [Exponential Distribution Proofs](https://real-statistics.com/other-key-distributions/exponential-distribution/exponential-distribution-proofs/): The proof that the exponential distribution is memoryless and the proof of the connection between the exponential and Poisson distributions.
- [Inverse Gamma Function](https://real-statistics.com/other-key-distributions/gamma-function/inverse-gamma-function/): Describes how to compute the inverse(s) of the gamma function. Includes examples and an Excel worksheet function that returns the inverse gamma function.
- [QAT Access](https://real-statistics.com/qat-access/): Describes how to customize Excel's Quick Access Toolbar (QAT) so that you can access Real Statistics data analysis tools in a single click.
- [Desc - Descriptive Statistics](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/desc-descriptive-statistics/): Describes in detail the Descriptive statistics option of Real Statistics' Excel-based Descriptive Statistics and Normality data analysis tool.
- [Desc - Outliers and Missing Data](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/desc-outliers-and-missing-data/): Describes in detail the Outliers and Missing Data option of Real Statistics' Excel-based Descriptive Statistics and Normality data analysis tool.
- [Solver](https://real-statistics.com/matrices-and-iterative-procedures/solver/): Explains how to use Excel's Solver tool. An example is given for finding regression coefficients via least squares method.
- [Iterative Proportional Fitting Procedure (IPFP)](https://real-statistics.com/matrices-and-iterative-procedures/iterative-proportional-fitting-procedure-ipfp/): How to use the Iterative Proportional Fitting Procedure (IPFP) to solve problems of independence testing. We provide examples for both 2 and 3 dimension cases.
- [Excel's Goal Seek](https://real-statistics.com/matrices-and-iterative-procedures/goal-seeking-and-solver/): Describes how to use Excel's Goal Seek. Examples are given for finding the roots of a polynomial and calculating eigenvalues and eigenvectors.
- [Determinant of a Square Matrix](https://real-statistics.com/matrices-and-iterative-procedures/determinants-and-simultaneous-linear-equations/): Describes how to calculate the determinant of a square matrix by hand, and also how to do it in Excel. Examples are given and a worksheet function is explained.
- [Excel Capabilities](https://real-statistics.com/excel-capabilities/): Describes Excel functions and other capabilities that are useful for statistical analysis. Includes pure Excel substitutes for Real Statistics functions.
- [Keyboard Shortcuts](https://real-statistics.com/excel-capabilities/keyboard-shortcuts/): Provides a list of Excel keyboard shortcuts that are useful for statistical analysis, along with a description of what the shortcut does
- [Chart standard errors of the mean](https://real-statistics.com/excel-capabilities/chart-standard-errors/): Describes how to create graphs that show vertical bars to depict the interval around the mean of one standard error using Excel’s charting capabilities.
- [Creating Box Plots with Outliers in Excel](https://real-statistics.com/excel-capabilities/creating-box-plot-outliers-manually/): Describes how to manually, step-by-step, create box plots with outliers in Excel. An example is provided to make the steps clearer
- [Creating Dot Plots in Excel](https://real-statistics.com/excel-capabilities/creating-dot-plots-in-excel/): Describes how to create a dot plot manually in Excel using Excel's charting capabilities. Provides step-by-step instructions.
- [Creating Simple Box Plots in Excel](https://real-statistics.com/excel-capabilities/special-charting-capabilities/): Describes how to create simple box plots using standard Excel charting capabilities. Examples are given to demonstrate the step-by-step process.
- [Table Lookup](https://real-statistics.com/excel-capabilities/table-lookup/): Describes various table lookup procedures that can be used in Excel, as well as additional functions provided by the Real Statistics Resource Pack.
- [Arrays as an argument in an Excel formula](https://real-statistics.com/excel-capabilities/array-arguments-in-excel-formulas/): Describes how Excel treats arrays that are not cell ranges when they are used as an argument in an Excel worksheet formula
- [Built-in Statistical Functions](https://real-statistics.com/excel-capabilities/built-in-statistical-functions/): List of Excel's statistics worksheet functions, including those for descriptive statistics, t-distribution, chi-square, regression and correlation.
- [Excel Conditional Functions](https://real-statistics.com/excel-capabilities/excel-conditional-functions/): Brief description of Excel's conditional worksheet functions useful in statistics, including IF, IFS, SUMIF, SUMIFS, COUNTIF, COUNTIFS, SWITCH, MINIFS, MAXIFS.
- [Miscellaneous Built-in Functions](https://real-statistics.com/excel-capabilities/built-in-excel-functions/): Description of Excel functions useful in statistics, including mathematical, summation, matrix, combinatorial, table lookup and dynamic array functions.
- [Table Lookup Functions](https://real-statistics.com/excel-capabilities/table-lookup-functions/): Describes how to perform table lookup in Excel using the worksheet functions INDEX, MATCH, OFFSET, and XLOOKUP. Examples are provided.
- [Sampling using Real Statistics Capabilities](https://real-statistics.com/sampling-distributions/sampling/sampling-using-real-statistics/): Shows how to use Real Statistics capabilities to create a random sample in Excel. Both sampling with and without replacement are explored.
- [Simulating a Distribution](https://real-statistics.com/sampling-distributions/simulation/simulating-a-distribution/): Describes how to use Monte Carlo simulation in Excel to estimate the pdf of a distribution. E.g. number of throws of a die to get all 6 outcomes.
- [Cox-Stuart Test](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/cox-stuart-test/): Describes how to conduct a Cox-Stuart test to determine whether a time series has an increasing or decreasing trend. Excel software and example are provided.
- [Sampling](https://real-statistics.com/sampling-distributions/sampling/): Shows how to use the Excel ToolPak and worksheet functions to create a random sample. Both sampling with and without replacement are explored.
- [Gamma Function](https://real-statistics.com/other-key-distributions/gamma-function/): Describes the gamma function, which is used to define a number of common probability distribution functions. It also described how to use this function in Excel
- [Winning Wordle in Three Tries](https://real-statistics.com/wordle-strategy/winning-wordle-in-three-tries/): Describe the strategy for optimizing the chances of guessing Wordle's target word within 3 tries. In particular, we show the best guesses after "slate".
- [Best Initial Guesses from the full Wordle Dictionary](https://real-statistics.com/wordle-strategy/best-second-guess-full-wordle-dictionary/): Describes how to make your best first and second guesses in Wordle when you can choose any 5 letter word: find the word that has the most non-zero patterns.
- [Generalized Pareto Distribution](https://real-statistics.com/other-key-distributions/pareto-distribution/generalized-pareto-distribution/): Provides the formulas for the pdf, cdf, and inverse of the Generalized Pareto distribution and shows how to calculate these in Excel. Includes key properties.
- [Tukey’s Test for Additivity](https://real-statistics.com/two-way-anova/two-factor-anova-without-replication/tukeys-test-for-additivity/): Describes how to perform Tukey’s Test for Additivity (in Excel) to determine whether the interaction effect is significant for two-way ANOVA w/o replication.
- [McNemar Test Effect Size and Power](https://real-statistics.com/non-parametric-tests/mcnemars-test/mcnemar-test-effect-size-and-power/): Describes how to calculate the effect size, power, and minimum sample size for McNemar's test. Provides examples using Excel.
- [Goodness-of-Fit to a Distribution](https://real-statistics.com/chi-square-and-f-distributions/goodness-of-fit/goodness-of-fit-to-a-distribution/): Describes how to use the chi-square test for goodness of fit of observeddata to a distribution using Excel. Also explores the Poisson index of dispersion.
- [Assumptions for Two-Sample t-Test](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/assumptions-for-two-sample-t-test/): Provides information about the assumptions for the two-sample t-test; in particular, the impact of violations on the type I error.
- [Double Integration Examples](https://real-statistics.com/other-mathematical-topics/integration/double-integration-examples/): This webpage provides examples of how to use the Real Statistics INTEGRAL2 worksheet function to perform double integration in Excel using numerical analysis.
- [Numerical Double Integration](https://real-statistics.com/other-mathematical-topics/integration/numerical-double-integration/): Describes how to estimate the value of a double integral using numerical analysis. Includes the case where the limits of the inner integral are functions.
- [Method of Moments: GPD](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-gpd/): Describes how to estimate the parameters of a Generalized Pareto distirbution that best fits some data using the method of moments. Includes an Excel example.
- [Moderation Analysis](https://real-statistics.com/multiple-regression/moderation-analysis/): How to conduct Moderation Analysis in Excel to determine how the relationship between independent & dependent variables changes based on a moderating variable.
- [Seasonal Kendall Test](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/mann-kendall-test/seasonal-kendall-test/): Describes how to conduct the Seasonal Kendall test to detect a trend for seasonal data in Excel. An example is worked out and software is provided.
- [Minimizing Expected Guesses for Wordle](https://real-statistics.com/wordle-strategy/minimizing-expected-tries-for-wordle/): We present strategies for minimizing the expected number of guesses when playing Wordle. Includes strategy for maximizing probability of winning in 3 guesses.
- [Bootstrapping](https://real-statistics.com/non-parametric-tests/bootstrapping/): How to create a bootstrap sample for any parameter. Also describes how to calculate a bootstrap confidence interval. Incl.Excel examples and worksheet functions
- [Jackknife](https://real-statistics.com/non-parametric-tests/jackknife/): Describes how to create a jackknife sample for any parameter. Also describes how to calculate the standard error. Incl.Excel examples and worksheet functions.
- [Refinements to Best Wordle Second Guess](https://real-statistics.com/wordle-strategy/refinements-to-best-wordle-second-guess/): Describes how to choose a second guess in Wordle if our primary goal is to win in 3 tries, but our secondary goal, failing this, is to win in at most 4 tries.
- [Fitting Data to a Cauchy Distribution](https://real-statistics.com/distribution-fitting/fitting-data-to-a-cauchy-distribution/): Describes how to use weighted order statistics to estimate the mu and sigma parameters of a Cauchy distribution that fits data.
- [Data Table with Two Variables](https://real-statistics.com/excel-environment/excels-data-table-facility/data-table-with-two-variables/): Describes how to use Excel's Data Table capability based on a formula f(x,y) in two variables. Examples are provided to illustrate key points.
- [Benford Distribution](https://real-statistics.com/other-key-distributions/benford-distribution/): Provides a brief description of Benford's law and the Benford distribution and when it is used, especially for fraud detection.
- [Benford Distribution Fitting Support](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-benford-distribution/benford-distribution-fitting-support/): Describes how to test (KS and AD tests) whether data follows Benford's rule using Real Statistics worksheet functions in Excel.
- [Goodness-of-fit for Benford Distribution](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-benford-distribution/): Describes how to test whether data follows Benford's rule using the Chi-square test, KS test, and AD test. Excel functions and examples are included.
- [Gradient Descent Examples](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/gradient-descent/gradient-descent-examples/): Describes how to use the Real Statistics MGRADIENT and MGRADIENTX worksheet functions to find the value X that minimizes f(X) in Excel.
- [Gradient Descent](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/gradient-descent/): Describes the gradient descent algorithm for finding the value of X that minimizes the function f(X), including steepest descent and backtracking line search.
- [Nelder-Mead Optimization](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/nelder-mead-optimization/): Describes how to apply the Nelder-Mead algorithm to find a local minimum, An Excel example and Excel worksheet function are provided
- [GoF ICF Multivariate Normal Distribution](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/gof-icf-multivariate-normal-distribution/): Tutorial on goodness-of-fit tests in Excel based on the characteristic function. Examples are provided for multivariate normal distributions.
- [Bradley–Terry Model](https://real-statistics.com/reliability/bradley-terry-model/): Describes how to create a Bradley-Terry model based on pairwise data using an iterative algorithm. Includes an Excel example and worksheet functions.
- [Real Statistics Data Table with Two Variables](https://real-statistics.com/real-statistics-environment/real-statistics-data-table-capabilities/real-statistics-data-table-with-two-variables/): Describes Real Statistics worksheet functions that provide capabilities similar to Excel's Data Table facility for two variables
- [Method of Moments: Negative Binomial Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-negative-binomial-distribution/): Describes how to estimate the alpha and beta parameters of the negative binomialdistribution that fits a set of data using the method of moments in Excel.
- [Greyscale](https://real-statistics.com/real-statistics-environment/colors/greyscale/): Describes colors in grayscale and how to represent these in Excel. Also describes how to convert a color image to grayscale.
- [Strategy for Minimizing Wordle Expectation](https://real-statistics.com/wordle-strategy/strategy-for-minimizing-wordle-expectation/): Provides a table for strategies 1 and 2 for minimizing the expected number of guesses required to win at Wordle in 5 guesses or fewer.
- [Minimum Expectation Strategy for Winning Wordle in 3 Guesses](https://real-statistics.com/wordle-strategy/minimum-expectation-strategy-for-winning-wordle-in-3/): Provides a table for strategies 3 and 4 for maximizing the probability of winning Wordle in 3 tries while minimizing the expected number of guesses.
- [Multivariate Normal Distribution and GHK Algorithm](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-normality-functions/multivariate-normal-distribution-ghk-algorithm/): Describes how to use the GHK algorithm to calculate the multivariate normal cumulative distribution function. Includes Excel examples and worksheet functions.
- [M/G/infinity Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-g-infinity-queueing-model/): Describes the M/M/infinity queueing model and provides formulas for various characteristics of this model, and explains how to calculate them in Excel.
- [GoF ICF Uniform & Exponential](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/gof-icf-uniform-exponential/): Tutorial on goodness-of-fit tests in Excel based on the characteristic function. Examples are provided for the uniform and exponential distributions.
- [Goodness of Fit Tests based on the Characteristic Function](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/): Tutorial on goodness-of-fit tests in Excel based on the characteristic function. Examples provided for normal, uniform, Laplace, Weibull, etc. distributions.
- [GoF ICF Laplace & Cauchy](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/gof-icf-laplace-cauchy/): l on goodness-of-fit tests in Excel based on the characteristic function. Examples are provided for the Laplace and Cauchy distributions.Tutoria
- [GoF ICF Gumbel & Weibull](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/gof-icf-gumbel-weibull/): Tutorial on goodness-of-fit tests in Excel based on the characteristic function. Examples are provided for the Gumbel and Weibull distributions.
- [GoF ICF Logistic Distribution](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/gof-icf-logistic-distribution/): Tutorial on goodness-of-fit tests in Excel based on the characteristic function. Examples are provided for the logistic distribution
- [Holt’s Linear Trend with Damping](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/holt-linear-trend/holts-linear-trend-with-damping/): Tutorial on how to conduct Holt's Linear Trend with damping forecasting in Excel. Examples and data analysis tools are provided and explained..
- [Weighted Variance, Standard Deviation, and Covariance](https://real-statistics.com/descriptive-statistics/measures-variability/weighted-variance-standard-deviation-and-covariance/): Describes how to calculate the weighted variance, standard deviation, and covariance in Excel for both reliability and frequency weights.
- [Bayesian t Test Tools](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-t-test-tools/): Describes various Excel worksheet functions provided by Real Statistics to perform Bayesian t-tests. A data analysis tool is also provided and various examples.
- [Bayesian Two-Sided Testing Examples](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-two-sided-testing-examples/): Gives examples of how to use the unit information and JZS Cauchy priors to perform two-sided hypothesis testing for normally distributed data in Excel.
- [Bayesian Independence Testing Support](https://real-statistics.com/bayesian-statistics/bayesian-independence-testing/bayesian-independence-testing-support/): Describes Excel worksheet functions and data analysis tools provided by the Real Statistics Resource Pack to perform Bayesian independence testing.
- [Multiple Signed-Ranks Tests](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/multiple-signed-ranks-tests/): Describes how to perform multiple Wilcoxon signed-rank tests in Excel while taking care of familywise error. Examples and Excel capabilities are provided
- [Multiple Mann-Whitney Tests](https://real-statistics.com/non-parametric-tests/mann-whitney-test/multiple-mann-whitney-tests/): Describes how to perform multiple Mann-Whitney tests in Excel while taking care of familywise error. Examples and Excel capabilities are provided
- [Rational Numbers in Qn](https://real-statistics.com/other-mathematical-topics/rational-numbers/rational-numbers-in-qn/): Using properties of coprime integers, we list rational numbers in (0,1) whose numerator and denominator are less than n. Includes Excel functions and examples.
- [Converting a Fraction to a Decimal](https://real-statistics.com/other-mathematical-topics/rational-numbers/converting-a-fraction-to-a-decimal/): Describes how to put a fraction in decimal form. Includes examples and Excel worksheet functions for doing this. Describes terminating and repeating decimals.
- [Graphing y = f(x)](https://real-statistics.com/real-statistics-environment/real-statistics-lambda-capabilities/graphing-y-fx/): Describes how to draw a graph of a function y = f(x) in one variable using Excel's charting capability and a Real Statistics data analysis tool
- [Excel Sorting Formulas](https://real-statistics.com/excel-environment/sorting-and-filtering-functions/excel-sorting-formulas/): Describes how to sort & remove duplicates in Excel using Excel tricks. Better approaches are available from Real Statistics and the latest Excel versions.
- [CEM 1-to-1 Example](https://real-statistics.com/matching/coarsened-exact-matching/cem-1-to-1-example/): Describes how to use the Real Statistics Coarsened Exact Matching data analysis tool (with 1-to-1 matching). This is done via an example in Excel.
- [PSM Example](https://real-statistics.com/matching/propensity-score-matching/psm-example/): Describes how to use the Real Statistics Propensity Score Matching data analysis tool. This is done via an example in Excel.
- [Bayesian t Test Sample Size](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-t-test-sample-size/): Determine the effect size needed to achieve a given level of support for a hypothesis for a given sample size. Also find the sample size needed in Excel.
- [Bayesian t Sample and Effect Size](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-t-sample-and-effect-size/): Provides tables of effect sizes needed to achieve a given level of support for a hypothesis for a given sample size, as well as the sample size needed in Excel.
- [Fitting Zero-Truncated Poisson Distribution](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-poisson-distribution/fitting-zero-truncated-poisson-distribution/): How to estimate the lambda parameter of a Zero-truncated Poisson distribution that best fits a data set using MoM & MLE in Excel. Includes examples & software.
- [Spearman's Correlation Testing using a Fisher Transformation](https://real-statistics.com/correlation/spearmans-rank-correlation/spearmans-correlation-testing-fisher-transformation/): How to test in Excel whether a population's Spearman's correlation coefficient is significantly different from some value using a Fisher transformation
- [Real Statistics Support for CEM](https://real-statistics.com/matching/coarsened-exact-matching/real-statistics-support-for-cem/): Describes the various Excel worksheet functions used to perform Coarsened Exact Matching. These are also used by the Real Statistics CEM data analysis tool.
- [CEM Example](https://real-statistics.com/matching/coarsened-exact-matching/cem-example/): Describes how to use the Real Statistics Coarsened Exact Matching data analysis tool (with weights. This is done via an example in Excel.
- [Numerical Differential Equations Support](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/numerical-differential-equations-support/): Describes how to solve differential equations numerically in Excel using Real Statistics worksheet functions. Examples and Excel function are provided.
- [More Numerical Differential Equation Methods](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/more-numerical-differential-equation-methods/): Describes how to solve differential equations using Euler's backward method, the trapeziod method or Runge-Kutta (RK2 and RK4). Includes Excel examples.
- [Euler's Method ODE](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/eulers-method-ode/): Describes how to solve differential equations using Euler's forward method. An example of how to do this in Excel is given and explained.
- [Simultaneous Differential Equations](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/simultaneous-differential-equations/): Describes how to solve simultaneous differential equations in Excel using the Real Statistics add-in. Examples are provided to illustrate the methodology.
- [Second Order Differential Equations](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/second-order-differential-equations/): Describes how to solve second order differential equations in Excel using the Real Statistics add-in. Examples are provided to illustrate the methodology.
- [Yuen-Welch's Test](https://real-statistics.com/students-t-distribution/problems-data-t-tests/yuen-welchs-test/): Describes how to conduct the Yuen-Welch Test in Excel. This test is useful when both the normality and equal variances assumptions for the t-test are not met.
- [Data Analysis Tool for Other Two Sample Tests](https://real-statistics.com/students-t-distribution/problems-data-t-tests/data-analysis-tool-for-other-two-sample-tests/): Describes how to use the Other Two Sample Tests data analysis tool to conduct the Trimmed Means t Test, Yuen-Welch's Test or Fligner-Policello test in Excel.
- [Trimmed Means t Test](https://real-statistics.com/students-t-distribution/problems-data-t-tests/trimmed-means-t-test/): How to conduct the Trimmed Means t Test in Excel. This test is useful when the normality assumption is not met, especially due to the presence of outliers.
- [Second-order Difference Equations](https://real-statistics.com/other-mathematical-topics/first-order-difference-equations/second-order-difference-equation/): Describes how to solve second-order difference equations. Also explains how to use Excel to obtain the solution. Includes worksheet function and example.
- [Differential Equations Analysis Tool](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/differential-equations-analysis-tool/): Describes how to use Real Statistics data analysis tool to solve first-order and second-order differential equations in Excel.
- [Length of a Curve](https://real-statistics.com/other-mathematical-topics/integration/length-of-a-curve/): Describes how to calculate the length of a curve in Excel using aworksheet function supplied by the Real Statistics Resource Pack.
- [Integration using Partial Fractions](https://real-statistics.com/other-mathematical-topics/integration/integration-partial-fractions/): Describes various techniques for evaluating integrals of rational expressions (i.e. quotients of quadratic polynomials) using partial fractions.
- [Quadratic Integrals](https://real-statistics.com/other-mathematical-topics/integration/quadratic-integrals/): Provides numerous examples of how to evaluate an integral whose integrand contains a quadratic polynomial. Uses substitution and integration by parts.
- [Integration by Parts](https://real-statistics.com/other-mathematical-topics/integration/integration-by-parts/): Describes how to use integration by parts. Includes various trig reduction properties and integrals involving quadratic polynomials.
- [Integration Techniques](https://real-statistics.com/other-mathematical-topics/integration/integration-techniques/): Describes some basic analytic integration formulas, including those from trigonometry. plus basic techniques (e.g. substitution and integration by parts).
- [Ellipse: Area and Perimeter](https://real-statistics.com/other-mathematical-topics/integration/ellipse-area-and-perimeter/): Describes how to calculate the area and perimeter of an ellipse. Provides formulas as well as examples and worksheet functions in Excel.
- [First-Order Difference Equations](https://real-statistics.com/other-mathematical-topics/first-order-difference-equations/): Describes how to solve first-order difference equations by hand. Also explains how to use Excel to obtain the solution. Includes worksheet function and example.
- [Basic Concepts for ANOVA](https://real-statistics.com/one-way-analysis-of-variance-anova/basic-concepts-anova/): Review of the basic concepts behind the analysis of variance (ANOVA) and how to perform ANOVA tests in Excel. Numerous examples are provided.
- [Grubbs' Test Data Analysis Tool](https://real-statistics.com/students-t-distribution/identifying-outliers-using-t-distribution/grubbs-test-data-analysis-tool/): Describes how to use the Grubbs option of the Real Statistics Descriptive Statistics data analysis tool to carry out Grubbs' test and ESD test in Excel.
- [Generalized Extreme Studentized Deviate Test](https://real-statistics.com/students-t-distribution/identifying-outliers-using-t-distribution/generalized-extreme-studentized-deviate-test/): Describes how to identify outliers using the Generalized Extreme Studentized Deviate (ESD) Test (extension to Grubbs' test) in Excel. Incl. software & examples.
- [Grubbs' Test](https://real-statistics.com/students-t-distribution/identifying-outliers-using-t-distribution/grubbs-test/): Describes how to identify outliers using Grubbs' test in Excel. Describes the Real Statistics GIBBS function for doing this. Software and examples included.
- [CI for Effect Sizes d* and g*](https://real-statistics.com/students-t-distribution/confidence-interval-effect-size-power/ci-for-effect-sizes-d-and-g/): Shows how to estimate confidence intervals for Cohen's d* and Hedges' g*, effect sizes used with the t-test for two independent samples with unequal variances.
- [Multiple t-Tests](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/multiple-t-tests/): Describes how to perform multiple independent sample t-tests in Excel while taking care of familywise error. Examples and Excel capabilities are provided.
- [Two Sample t-Test Proof](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/two-sample-t-test-advanced/): Provides a proof of Property 1 of Two Sample t-Test with Equal Variances, which is the basis of hypothesis testing of two independent samples.
- [Equivalence Testing (TOST)](https://real-statistics.com/students-t-distribution/equivalence-testing-tost/): Describes how to conduct two one-sided t tests (TOST) in Excel to determine whether two populations are equivalent. Examples are included.
- [Identifying Outliers using t Distribution](https://real-statistics.com/students-t-distribution/identifying-outliers-using-t-distribution/): Tutorial on how to identify outliers using Grubbs' test and its extensions (i.e. the ESD test) in Excel. Software and examples.
- [Cauchy Distribution](https://real-statistics.com/students-t-distribution/cauchy-distribution/): Describes the Cauchy distribution and how to use it in Excel. This distribution is unusual since the mean, variance, skewness and kurtosis are undefined.
- [Non-standardized t distribution](https://real-statistics.com/students-t-distribution/non-standardized-t-distribution/): Describes the key properties of the non-standardized (aka three-parameter) t distribution and how to calculate the pdf and cdf in Excel.
- [Studentized Range Distribution](https://real-statistics.com/students-t-distribution/studentized-range-distribution/): Brief introduction to the studentized range distribution and how to calculate its values and its critical values in Excel.
- [Sample Size for t Test based on Confidence Interval](https://real-statistics.com/students-t-distribution/sample-size-t-test-using-confidence-interval/): Describes the sample size required for a one-sample t test based on the width of the confidence interval. Show how to do this using Excel's Goal Seek.
- [Sample size requirements for t tests](https://real-statistics.com/students-t-distribution/sample-size-requirements-t-tests/): Describes how to determine the sample size required to achieve a target power for the t tests. Includes examples and Excel add-in software.
- [Noncentral t Distribution](https://real-statistics.com/students-t-distribution/noncentral-t-distribution/): Describes the Noncentral t Distribution and how to calculate the cumulative distribution (cdf) and probability distribution (pdf) function values in Excel.
- [When t test assumptions are violated](https://real-statistics.com/students-t-distribution/problems-data-t-tests/): How to address problems with data (outliers, lack of normality or symmetry) when performing a t test, including non-parametric tests and transformations.
- [Two Independent Samples t-Test](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/): Tutorial on the two independent sample t-test, including how to conduct the test in Excel, effect sizes, confidence intervals, power, and sample size.
- [Student's t Distribution](https://real-statistics.com/students-t-distribution/): Tutorial on the t distribution and how to perform the various t-tests in Excel. Also includes other tests that rely on the t distribution (e.g. Grubbs' test).
- [Binomial and Related Distributions](https://real-statistics.com/binomial-and-related-distributions/): Introduces the binomial and related distributions (incl. proportion, negative binomial, geometric, hypergeometric, beta, multinomial and Poisson distributions).
- [Proportion Parameter Confidence Interval](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/proportion-parameter-confidence-interval/): Describes various estimates of a confidence interval for the proportion parameter and how to calculate them in Excel. Includes an Excel example.
- [Cohen's h Effect Size](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/cohens-h-effect-size/): Describes Cohen's h, an effect size for the proportion parameter; used in proportion testing. Also, shows how to calculate Cohen's h in Excel.
- [Two-sample Proportion Testing](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/two-sample-proportion-testing/): Describes how to perform a two-sample proportion test in Excel using a normal approximation. Includes a step-by-step example to illustrate the concepts.
- [One-sample Proportion Testing](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/one-sample-proportion-testing/): Describes how to perform a one-sample proportion test in Excel. Includes examples. Also explains how to estimate the confidence interval.
- [Proportion Distribution Basic Concepts](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/proportion-distribution-basic-concepts/): Describes the basic properties of the proportion distribution; in particular its relationship with the binomial and normal distributions
- [Runs](https://real-statistics.com/binomial-and-related-distributions/runs/): Explains how to calculate the probability of a run of at least r (or at least r heads) in n tosses of a coin using recursion in Excel.
- [Poisson Distribution - Proof](https://real-statistics.com/binomial-and-related-distributions/poisson-distribution/poisson-distribution-advanced/): Proof of Property 1 of Poisson Distribution, namely that a Poisson distribution can be approximated by a normal distribution.
- [Skellam Distribution](https://real-statistics.com/binomial-and-related-distributions/poisson-distribution/skellam-distribution/): Described the Skellam distribution and its relationship to the Poisson distribution. Shows how to use this distribution to find the odds for sporting games.
- [Poisson Distribution](https://real-statistics.com/binomial-and-related-distributions/poisson-distribution/): Describes how to use the Poisson distribution as well as the relationship with the binomial and normal distributions. Also describes key functions in Excel
- [Multinomial Distribution](https://real-statistics.com/binomial-and-related-distributions/multinomial-distribution/): Describes how to use the multinomial function and multinomial distribution in Excel. Examples and a new Excel worksheet function are provided.
- [Beta Prime Distribution](https://real-statistics.com/binomial-and-related-distributions/beta-distribution/beta-prime-distribution/): Describes the probability of the odds of success on a single trial in Excel for a specific sample size & number of successes using the beta prime distribution.
- [Proportion Distribution and Testing](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/): Tutorial on how to use the proportion distribution to do one and two sample hypothesis testing in Excel. Provides software and examples.
- [Normal Approximation to Binomial Distribution](https://real-statistics.com/binomial-and-related-distributions/relationship-binomial-and-normal-distributions/): Describes how the binomial distribution can be approximated by the standard normal distribution; also shows this graphically.
- [Hypothesis Testing for Binomial Distribution](https://real-statistics.com/binomial-and-related-distributions/hypothesis-testing-binomial-distribution/): Provides various examples demonstrating how to use Excel functions to perform hypothesis testing using the binomial distribution.
- [Power & Sample Size Two-Sample Test](https://real-statistics.com/sampling-distributions/statistical-power-sample/power-sample-size-two-sample-test/): Describes how to calculate power and sample size for two-sample testing using the normal distribution. Excel software and examples are included.
- [Power and Sample Size Two-tailed Test](https://real-statistics.com/sampling-distributions/statistical-power-sample/power-sample-size-two-tailed-test/): Describes how to calculate power and sample size for two-tailed, one-sample testing using the normal distribution. Excel software and examples are included.
- [Sample Size Requirements for Tolerance Intervals](https://real-statistics.com/sampling-distributions/tolerance-interval/sample-size-requirements-for-tolerance-intervals/): Describes how to estimate the sample size requirements to produce a tolerance interval with given characteristics in Excel using Goal Seek.
- [Tolerance Interval Example](https://real-statistics.com/sampling-distributions/tolerance-interval/tolerance-interval-example/): Shows how to calculate a one-sided and two-sided tolerance interval in Excel. Two examples are presented to show how this is done.
- [Tolerance Interval](https://real-statistics.com/sampling-distributions/tolerance-interval/): Describes how to create a tolerance interval in Excel based on a normal distribution. Incl. Howe and Nutrella estimates. Examples and software are included.
- [Identifying Outliers and Missing Data](https://real-statistics.com/sampling-distributions/identifying-outliers-missing-data/): Identifies potential outliers and missing data in Excel using a data analysis tool found in the Real Statistics Resource Pack
- [Power and Sample Size using Real Statistics](https://real-statistics.com/sampling-distributions/power-sample-size-real-statistics/): Describes how to calculate power and sample size for one-sample and two-sample testing using the normal distribution. Excel software and examples are included.
- [Sequential Randomness](https://real-statistics.com/sampling-distributions/sequential-randomness/): Describes how to test whether a series is random using the mean of successive squared differences (MSSD). Examples and software are included.
- [Simulation](https://real-statistics.com/sampling-distributions/simulation/): Describes how to use random number generation techniques in Excel to simulate various distributions. Examples and software are provided.
- [Comparing two means when variances are known](https://real-statistics.com/sampling-distributions/comparing-two-means-with-known-variancesi/): Describes how to perform hypothesis testing in Excel for comparing two means when variances are known, using the normal distribution, i.e. two-sample z-test.
- [Hypothesis Testing using the Central Limit Theorem](https://real-statistics.com/sampling-distributions/one-sample-hypothesis-testing-central-limit-theorem/): How to perform on sample hypothesis testing of the mean using the Central Limit Theorem in Excel. Uses ZTEST, CONFIDENCE as well as Real Statistics functions.
- [Central Limit Theorem](https://real-statistics.com/sampling-distributions/central-limit-theorem/): Describes the Central Limit Theorem and the Law of Large Numbers. These are some of the most important properties used throughout statistical analysis.
- [Confidence Intervals for Sampling Distributions](https://real-statistics.com/sampling-distributions/confidence-intervals-sampling-distributions/): Describes how to calculate confidence interval for the sample mean. Provides some simple examples in Excel for how to accomplish this.
- [Standardized Effect Size](https://real-statistics.com/sampling-distributions/standardized-effect-size/): We describe Cohen's d effect size for one sample hypothesis testing of the mean. We include the default criteria for small, medium, and large effect size.
- [Single Sample Hypothesis Testing](https://real-statistics.com/sampling-distributions/single-sample-hypothesis-testing/): Describes how to perform one sample hypothesis testing using the normal distribution and standard normal distribution (via z-score).
- [Sampling Distributions - Advanced](https://real-statistics.com/sampling-distributions/basic-concepts-sampling-distributions/sampling-distribution-advanced/): Provides the proof of Theorem 1 in Basic Concepts of Sampling Distributions, relating sample mean to the mean of a normal population.
- [Basic Concepts of Sampling Distributions](https://real-statistics.com/sampling-distributions/basic-concepts-sampling-distributions/): Describes what a sample distribution is, and defines the sample mean and standard error of the mean in terms of the population mean and standard deviation.
- [Weibull with Multi-Censored Data](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/weibull-with-multi-censored-data/): Describes how to estimate Weibull distribution parameters that best fit a data set when there is multi-censored data. Uses MLE and Newton's method.
- [Fitting Generalized Gamma Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-generalized-gamma-distribution-parameters-via-mle/): Estimating generalized gamma distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples and software.
- [Distribution Fitting via MLE: Real Statistics Support](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/distribution-fitting-mle-real-statistics/): Describes Excel worksheet functions found in the Real Statistics Resource Pack for distribution fitting using the maximum likelihood approach.
- [Fitting Cauchy Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-cauchy-parameters-via-mle/): Describes how to find Cauchy distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Fitting Geometric Parameter via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-geometric-parameter-via-mle/): Describes how to find geometric distribution parameter that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Fitting Laplace Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-laplace-parameters-via-mle/): Describes how to find Laplace distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Fitting Logistic Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-logistic-parameters-via-mle/): Describes how to find logistic distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Fitting Gumbel Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-gumbel-parameters-via-mle/): Describes how to find Gumbel distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Fitting Lognormal Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-lognormal-distribution-via-mle/): How to estimate lognormal distribution parameters that best fits a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples and software.
- [Fitting a Normal Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-a-normal-distribution-via-mle/): Describes how to find normal distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Fitting Poisson Distribution](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-poisson-distribution/): Describes how to estimate the lambda parameter of a Poisson distribution that best fits a data set using MoM and MLE in Excel. Includes examples and software.
- [Fitting Binomial Distribution](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-binomial-distribution/): Describes how to find binomial distribution parameter p that best fit a data set using MoM and MLE techniques in Excel. Includes examples & worksheet functions.
- [Fitting PERT Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-pert-distribution-via-mle/): Describes how to estimate the a, b, and c parameters of the PERT distribution that fits a set of data using the MLE approach in Excel.
- [Fitting a Triangular Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-a-triangular-distribution-via-mle/): Describes how to estimate the a, b, and c parameters of the triangular distribution that fits a set of data using the MLE approach in Excel.
- [Fitting Uniform Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-uniform-parameters-via-mle/): Describes how to find uniform distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples and software.
- [Fitting Negative Binomial Distribution Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-negative-binomial-distribution-parameters-mle/): Describes how to estimate negative binomial distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples
- [Fitting Beta Distribution Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-beta-distribution-parameters-mle/): Describes how to estimate beta distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples and software.
- [Fitting Gamma Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-gamma-parameters-mle/): Describes how to find gamma distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples and software.
- [Fitting Weibull Parameters using MLE and Newton's Method](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-weibull-parameters-mle-newtons-method/): Describes how to fit a Weibull distribution to a data set using maximum likelihood estimation (MLE) based on Newton's method. We show how this is done in Excel.
- [Fitting Weibull Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-weibull-parameters-mle/): Describes how to find the Weibull parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Examples and software are provided.
- [Fitting Exponential Parameter via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-exponential-parameter-via-mle/): Describes how to use maximum likelihood estimation (MLE) to fit data to an exponential distribution. Describes the equivalence with the method of moments.
- [Method of Moments: Generalized Gamma Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-generalized-gamma-distribution/): How to estimate the alpha, beta, and delta parameters of the generalized gamma distribution that fit a data set using the method of moments approach in Excel.
- [Method of Moments: Lognormal Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-lognormal-distribution/): Describes how to estimate the mu and sigma parameters of the lognormal distribution that fits a set of data using the method of moments in Excel.
- [Method of Moments Support for PERT Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-pert-distribution/method-of-moments-support-for-pert-distribution/): Describes how to estimate the a, b, and c parameters of the PERT distribution that fits a set of data using the method of moments in Excel.
- [Method of Moments: PERT Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-pert-distribution/): Describes how to estimate the a, b, and c parameters of the PERT distribution that fits a set of data using the method of moments.
- [Method of Moments Support for Triangular Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-triangular-distribution/method-of-moments-support-for-triangular-distribution/): Describes how to estimate the a, b, and c parameters of the triangular distribution that fits a set of data using the method of moments in Excel.
- [Method of Moments: Triangular Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-triangular-distribution/): Describes how to estimate the a, b, and c parameters of the triangular distribution that fits a set of data using the method of moments approach in Excel.
- [Method of Moments: Uniform Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-uniform-distribution/): Describes how to estimate the alpha and beta parameters of the uniform distribution that fits a set of data using the method of moments in Excel.
- [Method of Moments: Beta Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-beta-distribution/): Describes how to estimate the alpha and beta parameters of the beta distribution that fits a set of data using the method of moments in Excel.
- [Method of Moments: Weibull Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-weibull/): Describes how to estimate the lambda parameter of the Weibull distribution that fits a set of data using the method of moments in Excel.
- [Method of Moments: Exponential Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-exponential-distribution/): Describes how to estimate the lambda parameter of the exponential distribution that fits a set of data using the method of moments in Excel.
- [Fitted Parameter CI Support](https://real-statistics.com/distribution-fitting/distribution-fitting-confidence-intervals/fitted-parameter-ci-support/): Describes how to determine the standard error and confidence interval for fitted distribution parameters in Excel using the Real Statistics Resource Pack.
- [Fitted Parameters Confidence Interval](https://real-statistics.com/distribution-fitting/distribution-fitting-confidence-intervals/fitted-parameters-confidence-interval/): Describes how to use bootstrapping simulation to estimate the confidence interval of estimated distribution parameters Incl. Excel examples & software.
- [Fitted Parameters Standard Error](https://real-statistics.com/distribution-fitting/distribution-fitting-confidence-intervals/fitted-parameters-standard-error/): Describes how to use the bootstrapping simulation approach to estimate the standard errors of estimated distribution parameters Incl. Excel examples & software.
- [Fitted Parameter Analytic CI](https://real-statistics.com/distribution-fitting/distribution-fitting-confidence-intervals/fitted-parameter-analytic-ci/): Describes how to use analytic approaches to estimate the standard error and confidence intervals for fitted distributed parameters.
- [Real Statistics Support for KDE](https://real-statistics.com/distribution-fitting/kernel-density-estimation/real-statistics-support-kde/): Shows how to use the Real Statistics software to perform Kernel Density Estimation in Excel. Step-by-step instructions and an example are provided.
- [KDE Example](https://real-statistics.com/distribution-fitting/kernel-density-estimation/kde-example/): Describes how to construct a kernel density estimation for some sample data and the associated plot. This is done using Excel.
- [Statistical Divergence](https://real-statistics.com/distribution-fitting/statistical-divergence/): Describes three types of divergence: Kullback-Leibler Divergence (KL), Jenson-Shannon Divergence, and the divergence statistic used for credit scoring
- [Distribution Fitting Confidence Intervals](https://real-statistics.com/distribution-fitting/distribution-fitting-confidence-intervals/): Tutorial on how to calculate the standard error and confidence intervals for estimated distribution parameters. Examples and software in Excel are included.
- [Distribution Fitting Tool](https://real-statistics.com/distribution-fitting/distribution-fitting-tool/): How to use the Distribution Fitting analysis tool to find the best-fit parameters for the normal, Weibull, exponential, beta, gamma, and uniform distribution.
- [Fitting a Weibull Distribution via Regression](https://real-statistics.com/distribution-fitting/fitting-weibull-regression/): Describes how to use regression to estimate Weibull parameter values that fit a data set. Excel examples are provided as well as Excel worksheet function.
- [Distribution Fitting via Maximum Likelihood](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/): Tutorial on how to use the maximum likelihood method for estimating the parameters of a distribution that fits a data set. Examples in Excel.
- [Method of Moments](https://real-statistics.com/distribution-fitting/method-of-moments/): Describes how to estimate the parameters of various distributions that fit a set of data using the method of moments in Excel.
- [CMH Analysis Tool](https://real-statistics.com/chi-square-and-f-distributions/cochran-mantel-haenszel/cmh-analysis-tool/): Describes how to conduct the Cochran-Mantel-Haenszel test using the Real Statistics data analysis tool in Excel. Also outputs Woolf's heterogeneity test.
- [CMH Example](https://real-statistics.com/chi-square-and-f-distributions/cochran-mantel-haenszel/cmh-example/): Describes a concrete example of the Cochran-Mantel-Haenszel test and shows how to conduct the test in Excel. Also includes Woolf’s Heterogeneity Test
- [CMH Test Basic Concepts](https://real-statistics.com/chi-square-and-f-distributions/cochran-mantel-haenszel/cmh-test-basic-concepts/): Describes the basic concepts of the Cochran-Mantel-Haenszel (CMH) test and Woolf's Heterogeneity test. Describes the formulas and calculations required.
- [Real Statistics support for independence testing with missing data](https://real-statistics.com/handling-missing-data/em-algorithm/independence-testing-tools-missing-data/): Describes the Real Statistics functions and data analysis tool for performing chi-square independence testing when there is missing data using the EM algorithm.
- [Independence testing with missing data](https://real-statistics.com/handling-missing-data/em-algorithm/independence-testing-with-missing-data/): Describes how to conduct the chi-square test of independence in Excel even when there is missing data. An example is given and free Excel software is provided.
- [Chi-square Post-hoc Functions](https://real-statistics.com/chi-square-and-f-distributions/independence-testing/chi-square-post-hoc-functions/): Describes the Real Statistics support for post-hoc testing after a chi-square test of independence. This consists of a variety of worksheet functions.
- [Independence Testing Follow-up](https://real-statistics.com/chi-square-and-f-distributions/independence-testing/independence-testing-follow-up/): Describes how to perform post-hoc testing after a significant chi-square test of independence. Examples and software are provided.
- [Power of Two Sample Variance Testing](https://real-statistics.com/chi-square-and-f-distributions/power-of-two-sample-variance-testing/): How to calculate the power of two sample variance testing and the sample size needed to achieve a specified power for such tests. Examples and Excel add-in.
- [Two Sample Hypothesis Testing to Compare Variances](https://real-statistics.com/chi-square-and-f-distributions/two-sample-hypothesis-testing-comparing-variances/): Describes how to determine whether the variances for two samples are significantly different using Excel's F.TEST function and Excel's data analysis tool.
- [F Distribution](https://real-statistics.com/chi-square-and-f-distributions/f-distribution/): Describes basic properties of the F distribution, esp. its relationship to the chi-square and t distributions. Shows how to use this distribution in Excel.
- [Confidence Intervals for Power and Effect Size for Chi-square Tests](https://real-statistics.com/chi-square-and-f-distributions/confidence-interval-power-effect-size-chi-square-test/): Describes how to calculate confidence intervals for effect size, noncentrality parameter and power for chi-square tests in Excel. Software &examples included.
- [Power of Chi-square Tests](https://real-statistics.com/chi-square-and-f-distributions/power-chi-square-tests/): Describes how to calculate the power of the chi-square goodness of fit and independence tests and the sample size requirements for these tests. Incl. examples.
- [2 x 2 Contingency Table Testing](https://real-statistics.com/chi-square-and-f-distributions/2-x-2-contingency-table-testing/): Describes the testing of 2 × 2 contingency tables for independence, incl. the chi-square test and Fisher & Boschloo exact tests. Includes a data analysis tool.
- [Boschloo Exact Test](https://real-statistics.com/chi-square-and-f-distributions/boschloo-exact-test/): Describes how to perform the Boschloo exact test. Also provides examples and worksheet functions associated with performing this test in Excel.
- [Fisher’s Exact Test](https://real-statistics.com/chi-square-and-f-distributions/fishers-exact-test/): Show how to calculate the Fisher exact test for independence using Excel. Includes the Freeman-Halton extension. Examples and software are provided.
- [One Sample Hypothesis Testing of the Variance](https://real-statistics.com/chi-square-and-f-distributions/one-sample-hypothesis-testing-variance/): We describe how to use the chi-square distribution to test whether the variance of a sample is equal to some value. We provide some examples in Excel.
- [Other Key Distributions](https://real-statistics.com/other-key-distributions/): Review of the uniform distribution, exponential distribution, gamma function, gamma distribution Weibull distribution, etc. in the Excel environment.
- [Discrete Uniform Distribution](https://real-statistics.com/other-key-distributions/uniform-distribution/discrete-uniform-distribution/): Provides a brief overview of the discrete uniform distribution. Key properties are given as well as the probability density & cumulative distribution functions.
- [Distribution Property Functions](https://real-statistics.com/other-key-distributions/distribution-property-functions/): Describes the Real Statistics functions that output the mean and variance of various distributions in the Excel environment.
- [Generalized Gamma Distribution](https://real-statistics.com/other-key-distributions/generalized-gamma-distribution/): Describes the generalized gamma distribution, its key properties, its relationship to other distributions, and how to use it in Excel.
- [Wakeby Distribution](https://real-statistics.com/other-key-distributions/wakeby-distribution/): Describes how to calculate the cdf, pdf, and inverse cdf for the Wakeby distribution in Excel. Provides Excel worksheet functions
- [Laplace Distribution](https://real-statistics.com/other-key-distributions/laplace-distribution/): Describes key properties of the Laplace distribution (pdf, cdf, mean, median, standard deviation, etc.) and how to use this distribution in Excel.
- [Logistic Distribution](https://real-statistics.com/other-key-distributions/logistic-distribution/): Describes key properties of the logistic distribution (pdf, cdf, mean, median, standard deviation, etc.) and how to use this distribution in Excel.
- [Gumbel Distribution](https://real-statistics.com/other-key-distributions/gumbel-distribution/): Describes key properties of the Gumbel distribution, the objective of this distribution and how to use this distribution in Excel
- [Survivability and the Weibull Distribution](https://real-statistics.com/other-key-distributions/survivability-weibull-distribution/): Describes how to characterize the survivability of components that follow a Weibull distribution, incl. MRL & survival plots. Examples and software are provided
- [Gamma Distribution](https://real-statistics.com/other-key-distributions/gamma-distribution/): A brief introduction to the gamma distribution in Excel, including a description of Excel functions and an example of how to use this distribution.
- [Gamma Function Advanced](https://real-statistics.com/other-key-distributions/gamma-function/gamma-function-advanced/): Provides proofs of properties described in the Gamma Function page as well as related functions, including lower/upper incomplete gamma function.
- [Rectified Normal Distribution](https://real-statistics.com/normal-distribution/rectified-normal-distribution/): Describes the rectified normal distribution and how to calculate its pdf, cdf, inverse function, mean and variance in Excel
- [Split Normal Distribution](https://real-statistics.com/normal-distribution/split-normal-distribution/): Describes the split normal distribution and how to calculate its pdf, cdf, inverse function and a number of properties using Excel.
- [Half-Normal Distribution](https://real-statistics.com/normal-distribution/half-normal-distribution/): Describes the half-normal distribution and how to calculate its pdf, cdf, inverse function and a number of properties in Excel.
- [Truncated Normal Distribution](https://real-statistics.com/normal-distribution/truncated-normal-distribution/): Describes the truncated normal distribution and how to calculate its pdf, cdf, inverse function and key properties in Excel
- [Log-normal Distribution](https://real-statistics.com/normal-distribution/log-normal-distribution/): How and when to use the log-normal distribution in Excel. Includes a description of Excel functions that calculate the pdf and cdf values of this distribution.
- [Standard Normal Distribution](https://real-statistics.com/normal-distribution/standard-normal-distribution/): Describes the standard normal distribution, i.e the normal distribution with mean 0 and standard deviation 1. Key properties and Excel functions are described.
- [Lilliefors Test for Normality](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/lilliefors-test-normality/): Describes how to perform the Lilliefors test for normality in Excel. Software, examples and a table of Lilliefors critical values are provided.
- [Statistical Tests for Normality and Symmetry](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/): Explains how to use statistical tests such as Shapiro-Wilk, Kolmogorov-Smirnov and Chi-square to determine whether data is normally distributed.
- [Analysis of Skewness and Kurtosis](https://real-statistics.com/tests-normality-and-symmetry/analysis-skewness-kurtosis/): Explains how to use the values of skewness (SKEW) and kurtosis in Excel to determine whether data is normally distributed, incl. Jarque-Bera test.
- [Histogram with Normal Curve Overlay](https://real-statistics.com/tests-normality-and-symmetry/histogram-with-normal-curve-overlay/): Describes how to create a histogram with a normal curve overlay in Excel. This can be used to determine whether data is normally distributed.
- [Order Statistics Applications](https://real-statistics.com/order-statistics/order-statistics-applications/): Describes three applications of order statistics: outlier detection, quality control, and reliability. Excel examples are provided.
- [Multiple Regression Analysis Theory](https://real-statistics.com/multiple-regression/multiple-regression-analysis/multiple-regression-analysis-detailed/): Provides proofs of properties related to multiple regression analysis. Includes the proof that the usual least-squares estimate of the coefficients is unbiased.
- [Interpreting Regression Coefficients](https://real-statistics.com/multiple-regression/multiple-regression-analysis/interpreting-regression-coefficients/): Describes how to interpret the regression coefficients of continuous and categorical (dummy) variables when using multiple linear regression
- [Alternative approach to multiple regression analysis](https://real-statistics.com/multiple-regression/multiple-regression-analysis/alternative-approach-multiple-regression-analysis/): We describe an alternative approach to performing multiple regression analysis in Excel using the F-test. Includes some theory and an example.
- [Sample Size Requirements for Multiple Regression](https://real-statistics.com/multiple-regression/multiple-regression-analysis/sample-size-multiple-regression/): Describes how big a sample is required to achieve 80% power at various values for R-square when doing multiple regression
- [Regression Forecasts with Seasonality](https://real-statistics.com/multiple-regression/multiple-regression-analysis/seasonal-regression-forecasts/): Describes how to perform a forecast with seasonality using Excel. Example is given showing how it is done using categorical variables.
- [Testing regression coefficients](https://real-statistics.com/multiple-regression/multiple-regression-analysis/testing-regression-coefficients/): Describes how to test whether any regression coefficient is statistically equal to some constant or whether two regression coefficients are statistically equal.
- [Categorical Coding for Regression](https://real-statistics.com/multiple-regression/multiple-regression-analysis/categorical-coding-regression/): Describes how to handle categorical variables in linear regression by using dummy variables. Implements these in an Excel add-in. Examples given.
- [Regression using Solver](https://real-statistics.com/multiple-regression/multiple-regression-analysis/regression-using-solver/): Describes how to use the Solver option of the Real Statistics Multiple Regression data analysis tool with certain types of data.
- [Multiple Regression using Matrices](https://real-statistics.com/multiple-regression/multiple-regression-analysis/multiple-regression-using-matrices/): Describes how to perform multiple linear regression using matrix operations in Excel. Also defines the hat matrix and regression residuals.
- [Multiple Regression Basic Concepts](https://real-statistics.com/multiple-regression/multiple-regression-analysis/multiple-regression-basic-concepts/): Describes some of the theoretical foundations for multiple linear regression. Includes a list of the assumptions for multiple regression,
- [Breusch-Godfrey and Newey-West Tool](https://real-statistics.com/multiple-regression/autocorrelation/breusch-godfrey-and-newey-west-tool/): Describes how to perform the Breusch-Godfrey test and calculate the Newey-West standard errors in Excel using a Real Statistics data analysis tool.
- [Cochrane-Orcutt Tool](https://real-statistics.com/multiple-regression/autocorrelation/cochrane-orcutt-tool/): Describes how to perform Cochrane-Orcutt regression to correct for autocorrelation using a Real Statistics data analysis tool; also includes Durbin-Watson test.
- [Newey-West Standard Errors](https://real-statistics.com/multiple-regression/autocorrelation/newey-west-standard-errors/): Describes how to calculate the Newey-West standard errors in Excel for multiple linear regression where autocorrelation is present. Includes a detailed example.
- [FGLS Method for Autocorrelation](https://real-statistics.com/multiple-regression/autocorrelation/fgls-method-for-autocorrelation/): Describes the feasible general least squares (FGLS) regression and how to implement this approach in Excel. This is useful when there is autocorrelation.
- [Cochrane-Orcutt Regression](https://real-statistics.com/multiple-regression/autocorrelation/cochrane-orcutt-regression/): Describes how to carry out the Cochrane-Orcutt procedure in Excel to address autocorrelation in linear regression. Example and software are provided.
- [Durbin-Watson Test](https://real-statistics.com/multiple-regression/autocorrelation/durbin-watson-test/): Describes how to use the Durbin-Watson statistic for testing first-order autocorrelation in regression models in Excel. Examples and software are provided.
- [Breusch-Godfrey Test](https://real-statistics.com/multiple-regression/autocorrelation/breusch-godfrey-test/): Describes how to conduct the Breusch-Godfrey (BG) Test in Excel to detect autocorrelation up to any predesignated order p. Example and software are provided.
- [Detecting Autocorrelation via Runs Test](https://real-statistics.com/multiple-regression/autocorrelation/detecting-autocorrelation-runs-test/): Describes how to use the one-sample Runs test to detect autocorrelation in Excel. An Excel example is included that demonstrates the procedure.
- [Detecting Autocorrelation Graphically](https://real-statistics.com/multiple-regression/autocorrelation/detecting-autocorrelation-graphically/): Describes how to detect autocorrelation by creating a graph of the residuals against a time-lagged version of these residuals. We show this in Excel.
- [Autocorrelation Introduction](https://real-statistics.com/multiple-regression/autocorrelation/autocorrelation-introduction/): Provides a brief introduction to autocorrelation, including the definition and the sources for it, as well as the problems for the regression model.
- [ANOVA Residuals](https://real-statistics.com/multiple-regression/anova-using-regression/anova-residuals/): Describes how to use dummy coding to create regression models that are equivalent to one-way and two-way ANOVA, thereby identifying the residuals for ANOVA.
- [Confidence and Prediction Intervals Proofs](https://real-statistics.com/multiple-regression/confidence-and-prediction-intervals/confidence-and-prediction-intervals-proofs/): Provides the proofs of the properties about confidence interval and prediction intervals for multiple linear regression models.
- [Multiple Regression without Intercept](https://real-statistics.com/multiple-regression/multiple-regression-without-intercept/): Explains how to perform multiple linear regression without a constant term in Excel. Includes examples, theory and software.
- [Regression through Origin in Excel](https://real-statistics.com/multiple-regression/multiple-regression-without-intercept/regression-wo-constant-in-excel/): Explains how to perform multiple linear regression without a constant term in Excel (i.e. regression through the origin). Includes examples and software.
- [WLS regression via OLS regression through the origin](https://real-statistics.com/multiple-regression/weighted-linear-regression/wls-regression-via-ols-regression-thru-the-origin/): Describes how to address heteroscedasticity by using a version of weighted regression based on OLS regression thru the origin. Examples & software are provided
- [Real Statistics Support for WLS regression](https://real-statistics.com/multiple-regression/weighted-linear-regression/real-statistics-support-for-wls-regression/): Describes how to use the Real Statistics Weighted Linear Regression data analysis tool and Excel-based functions provided by the Real Statistics Resource Pack.
- [LAD Regression Analysis Tool](https://real-statistics.com/multiple-regression/lad-regression/lad-regression-analysis-tool/): Describes how to calculate LAD regression coefficients and their standard errors and confidence intervals in Excel using the Real Statistics data analysis tool.
- [Standard Errors of LAD Regression Coefficients via Bootstrapping](https://real-statistics.com/multiple-regression/lad-regression/standard-errors-lad-regression-coefficients-bootstrapping/): Describes how to use bootstrapping to calculate the standard error of a parameter; shows how this is done for the LAD regression coefficients.
- [LAD Regression using IRLS Method](https://real-statistics.com/multiple-regression/lad-regression/lad-regression-irls-method/): Describes how to calculate the coefficients of a LAD regression model in Excel using iteratively reweighted least squares (IRLS). Examples are provided.
- [LAD Regression using Simplex Method](https://real-statistics.com/multiple-regression/lad-regression/lad-regression-simplex-method/): Describes how to calculate the coefficients of a LAD regression model in Excel using Solver's Simplex capability. Examples are provided.
- [LASSO Regression](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/lasso-regression/): Describes how to calculate the LASSO regression coefficients and LASSO Trace in Excel. Example and software are provided.
- [Ridge Regression Predictions](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/ridge-regression-predictions/): Describes how to make forecasts based on a Ridge regression model. Also shows how to calculate residuals and mean squared error. Excel examples.
- [Ridge Regression Analysis Tool](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/ridge-regression-analysis-tool/): Describes how to use the Real Statistics Ridge Regression data analysis tool. This tool implements Ridge regression in Excel.
- [Estimating Ridge Regression Lambda](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/estimating-ridge-regression-lambda/): Describes approaches, in Excel, for estimating the lambda value for Ridge regression, including k-fold cross-validation and a Ridge trace.
- [Ridge Regression Example](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/ridge-regression-example/): Describes how to perform Ridge Regression. Provides examples in Excel. Also provides Excel worksheet functions that streamline the task.
- [Ridge Regression Basic Concepts](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/ridge-regression-basic-concepts/): Provides the motivation behind Ridge Regression and describes how to conduct Ridge Regression. Includes a description of key formulas and properties
- [Real Statistics support for Mediation Analysis](https://real-statistics.com/multiple-regression/mediation-analysis/mediation-analysis-tool/): Describes how to use the Real Statistics Mediation Analysis data analysis tool to perform Mediation Analysis in Excel based on the approach of Baron and Kenny.
- [Sobel Test](https://real-statistics.com/multiple-regression/mediation-analysis/sobel-test/): Describes how to execute the Sobel test in Excel to perform Mediation Analysis based on the work of Baron and Kenny. An example and software are provided.
- [Mediation Analysis Basics](https://real-statistics.com/multiple-regression/mediation-analysis/mediation-analysis-basics/): Describes the basic approach to Mediation Analysis, and how to carry out the analysis in Excel. Example and software are provided.
- [Tobit Regression Technical Information](https://real-statistics.com/multiple-regression/tobit-regression/tobit-regression-technical-information/): Provides technical information about Tobit Regression. Explains how to estimate coefficients using MLE. This webpage uses calculus.
- [Real Statistic Support for Tobit Regression](https://real-statistics.com/multiple-regression/tobit-regression/real-statistic-support-for-tobit-regression/): Describes an Excel analysis tool that creates a Tobit model and Excel worksheet functions to estimate regression coefficients & censored/uncensored estimates.
- [Tobit Model Description](https://real-statistics.com/multiple-regression/tobit-regression/tobit-model-description/): Describes the Tobit regression model, including censored and uncensored characteristics. Includes pdf, cdf, and expectations.
- [Tobit Regression](https://real-statistics.com/multiple-regression/tobit-regression/): Tutorial on Tobit regression (aka censored linear regression) and describes how to build a Tobit model in Excel. Includes examples and software.
- [Constrained Linear Regression](https://real-statistics.com/multiple-regression/constrained-linear-regression/): Tutorial on how to perform multiple linear regression where there are constraints on the regression coefficients. Excel software and examples are included.
- [Mediation Analysis](https://real-statistics.com/multiple-regression/mediation-analysis/): Provides a tutorial on performing mediation analysis in Excel. Examples and software are provided
- [Ridge and LASSO Regression](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/): Tutorial on Ridge and LASSO regression. Explains the motivation behind these types of regression and how to carry them out in Excel. Incl. examples & software.
- [Least Absolute Deviation (LAD) Regression](https://real-statistics.com/multiple-regression/lad-regression/): Tutorial on how to perform least absolute deviation (LAD) regression in Excel using the Simplex and iterative reweighted least-squares (IRLS) methods.
- [Shapley-Owen Decomposition](https://real-statistics.com/multiple-regression/shapley-owen-decomposition/): Describes how to calculate the Shapley-Owen decomposition of the R-square parameter from multiple regression. Includes examples and Excel add-in.
- [Robust Standard Errors](https://real-statistics.com/multiple-regression/robust-standard-errors/): Describes how to calculate robust standard errors in Excel using the techniques of Huber-White to address heteroscedasticity. Includes examples and software.
- [Weighted Linear Regression](https://real-statistics.com/multiple-regression/weighted-linear-regression/): Described how to conduct weighted multiple linear regression in Excel; useful in addressing heteroskedasticity. Includes examples and software.
- [Heteroskedasticity](https://real-statistics.com/multiple-regression/heteroskedasticity/): Tutorial on the Heteroskedasticity assumption in multiple least-squares linear regression. Deals with testing and what to do when this assumption is not met.
- [Confidence intervals of effect size and power for regression](https://real-statistics.com/multiple-regression/confidence-intervals-effect-size-power-regression/): Describes how to calculate confidence intervals for effect size and power for regression in Excel. Software and examples are provided.
- [Multiple Regression](https://real-statistics.com/multiple-regression/): How to perform multiple regression in Excel, including effect size, residuals, collinearity, ANOVA via regression. Extra analyses provided by Real Statistics.
- [Cross Validation](https://real-statistics.com/multiple-regression/cross-validation/): Describes cross validation and the related concepts of predictive sum of squares and predictive R-square. Example and software are provided.
- [Statistical Power and Sample Size for Multiple Regression](https://real-statistics.com/multiple-regression/statistical-power-sample-size-multiple-regression/): Describes how to calculate the statistical power and sample size requirements for multiple regression in Excel. Software and examples are included.
- [Standardized Regression Coefficients](https://real-statistics.com/multiple-regression/standardized-regression-coefficients/): How to calculate standardized regression coefficients and how to calculate unstandardized regression coefficients from standardized coefficients in Excel.
- [Stepwise Regression](https://real-statistics.com/multiple-regression/stepwise-regression/): Describes how to perform stepwise regression in Excel. Various worksheet functions are described as well as a data analysis tool. Examples are included.
- [Testing the significance of extra variables on the model](https://real-statistics.com/multiple-regression/testing-significance-extra-variables-regression-model/): Testing the significance of adding or subtracting variables from the regression model (reduced vs complete model). Also Akaike’s information criterion, AIC.
- [Collinearity](https://real-statistics.com/multiple-regression/collinearity/): How to identify in Excel when collinearity occurs, i.e. when one independent variable is a non-trivial linear combination of the other independent variables.
- [Autocorrelation](https://real-statistics.com/multiple-regression/autocorrelation/): Describes the consequences of autocorrelation (aka serial correlation) on linear regression. Describes how to detect autocorrelation and how to address it.
- [Three Factor ANOVA using Regression](https://real-statistics.com/multiple-regression/three-factor-anova-using-regression/): How to use regression models in Excel to perform three factor analysis of variance (ANOVA) for both balanced and unbalanced models
- [Unbalanced Factorial ANOVA](https://real-statistics.com/multiple-regression/unbalanced-factorial-anova/): How to use regression models in Excel to perform analysis of variance (ANOVA) for samples of different sizes (unbalanced models).
- [ANOVA using Regression](https://real-statistics.com/multiple-regression/anova-using-regression/): Describes how to use Excel's tools for regression to perform analysis of variance (ANOVA). Shows how to use dummy (aka categorical) variables to accomplish this
- [Comparing slopes and intercepts](https://real-statistics.com/multiple-regression/comparing-slopes-and-intercepts/): Describes how to determine whether the slopes and intercepts for two or more regressions are equal. Gives an example in Excel.
- [Interaction](https://real-statistics.com/multiple-regression/interaction/): How to perform multiple regression analysis in Excel where interaction between variables is modeled.
- [Multiple Regression with Logarithmic Transformations](https://real-statistics.com/multiple-regression/multiple-regression-log-transformations/): Provides examples in Excel of how to use log transformations to create better fitting regression models. Incl. log-log, log-level, level-log transformations
- [Confidence and Prediction Intervals](https://real-statistics.com/multiple-regression/confidence-and-prediction-intervals/): Describes how to calculate the confidence and prediction intervals for multiple regression in Excel. Software and examples included.
- [Method of Least Squares for Multiple Regression](https://real-statistics.com/multiple-regression/least-squares-method-multiple-regression/): How to find the regression coefficients in Excel for the multiple regression line which is the best fit for data using the method of least squares.
- [Poisson Regression Analysis Tool](https://real-statistics.com/poisson-regression/poisson-regression-analysis-tool/): Describes how to use the Real Statistics Poisson Regression data analysis tool to create a Poisson Regression model from a data set.
- [Poisson Regression using Newton's Method](https://real-statistics.com/poisson-regression/poisson-regression-using-newtons-method/): Describes how to estimate the Poisson regression coefficients and their standard errors using Newton's method. Also provides Excel worksheet functions for them.
- [Poisson Regression using Solver](https://real-statistics.com/poisson-regression/poisson-regression-using-solver/): Describes how to calculate the coefficients for a Poisson regression model using Excel's Solver. Provides an example to show how this is done.
- [Poisson Regression Basic Concepts](https://real-statistics.com/poisson-regression/poisson-regression-basic-concepts/): Describes how to perform Poisson regression in Excel. Includes examples and free software for carrying out Poisson regression.
- [Poisson Regression](https://real-statistics.com/poisson-regression/): Tutorial on how to perform Poisson regression in Excel. Examples and free software are provided. Poisson regression is used with count data.
- [Comparing Poisson and Negative Binomial Regression Models](https://real-statistics.com/negative-binomial-regression/comparing-poisson-and-negative-binomial-regression-models/): Describes how to test in Excel whether there is a significant difference between a Poisson regression and Negative Binomial regression model.
- [Negative Binomial Regression Predictions](https://real-statistics.com/negative-binomial-regression/negative-binomial-regression-predictions/): Describes how to make predictions based on negative binomial regression models in Excel. Examples and worksheet functions are included.
- [Negative Binomial Regression Analysis Tool (Newton's Method)](https://real-statistics.com/negative-binomial-regression/negative-binomial-regression-analysis-tool-newtons-method/): Describes Newton's method version of Real Statistics' Negative Binomial Regression data analysis tool and its use to perform count regression in Excel.
- [Negative Binomial Regression Analysis Tool (Solver option)](https://real-statistics.com/negative-binomial-regression/negative-binomial-regression-analysis-tool-solver-option/): Describes Real Statistics' Negative Binomial Regression data analysis tool and how to use it to perform this type of count regression in Excel.
- [Creating a Negative Binomial Regression model using Solver](https://real-statistics.com/negative-binomial-regression/creating-a-negative-binomial-regression-model-using-solver/): Describes how to construct a negative binomial regression model in Excel using Solver. Provides an example and worksheet functions.
- [Negative Binomial Regression](https://real-statistics.com/negative-binomial-regression/): Tutorial on how to perform Negative Binomial regression in Excel. Examples and free software are provided. Neg Binomial regression is used with count data.
- [Negative Binomial Regression: Additional Insights](https://real-statistics.com/negative-binomial-regression/negative-binomial-regression-additional-insights/): Describes a simple Negative binomial regression example which provides some additional insights about this way of modeling count data.
- [Ordinal Regression Basic Concepts](https://real-statistics.com/ordinal-regression/ordinal-logistic-regression/): Describes various ways for building a logistic regression model in Excel (e.g. using Solver, multiple binary logistic models and proportional odds model).
- [Ordinal Regression](https://real-statistics.com/ordinal-regression/): Tutorial on ordinal logistic regression, Models are built using Excel's Solver and Newton's method. Excel examples and analysis tools are provided.
- [Real Statistics Multinomial Logistic Regression Capabilities](https://real-statistics.com/multinomial-ordinal-logistic-regression/real-statistics-functions-multinomial-logistic-regression/): Describes the functions and data analysis tool in the Real Statistics Resource Pack (Excel add-in) to create Multinomial Logistics Regression models in Excel.
- [Finding multinomial logistic regression coefficients using Newton's method](https://real-statistics.com/multinomial-ordinal-logistic-regression/finding-multinomial-logistic-regression-coefficients-using-newtons-method/): Describe how to create a multinomial logistic regression model using Newton's Method. An Excel add-in is also provided to carry out the calculations.
- [Finding multinomial logistic regression coefficients using Solver](https://real-statistics.com/multinomial-ordinal-logistic-regression/finding-multinomial-logistic-regression-coefficients-using-solver/): Describe how to calculate multinomial logistic regression coefficients and create a multinomial logistic regression model using Excel's Solver.
- [Multinomial Logistic Regression Forecasts](https://real-statistics.com/multinomial-ordinal-logistic-regression/multinomial-regression-using-binary-logistic-regression/multinomial-logistic-regression-forecasts/): Describes how to obtain forecasts based on multinomial logistic regression models. We provide examples in Excel along with explanations.
- [Multinomial regression using binary logistic regression](https://real-statistics.com/multinomial-ordinal-logistic-regression/multinomial-regression-using-binary-logistic-regression/): Describes how to estimate the multinomial logistic regression model coefficients by using multiple binary logistic regression models. Excel example is provided.
- [Multinomial Logistic Regression](https://real-statistics.com/multinomial-ordinal-logistic-regression/): Tutorial on multinomial logistic regression, Models are built using Excel's Solver and Newton's method. Excel examples and analysis tools are provided.
- [Basic Concepts of Multinomial Logistic Regression](https://real-statistics.com/multinomial-ordinal-logistic-regression/basic-concepts-of-multinomial-logistic-regression-basic-concept/): Describes basic concepts of multinomial logistic regression, their connection to binary logistic regression, & the use of Newton's method to find coefficients.
- [Runs Test with more than two categories](https://real-statistics.com/non-parametric-tests/one-sample-runs-test/runs-test-with-more-than-two-categories/): Describes how to perform a one-sample runs test in Excel when there are more than two categories. Examples and new Excel worksheet functions are provided
- [Two-Sample Runs Test](https://real-statistics.com/non-parametric-tests/two-sample-runs-test/): Describes how to perform the Two-Sample (Wald-Wolfowitz) Runs Test. Includes an example showing how to perform the test in Excel and a worksheet function.
- [Holt's Linear Trend](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/holt-linear-trend/): Tutorial on how to conduct Holt's Linear Trend forecasting in Excel. Examples and software are provided. Also shows how to use Solver to optimize the forecast.
- [Holt's Linear Trend Confidence Interval](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/holt-linear-trend/holts-linear-trend-confidence-interval/): Describes how to calculate the standard error and confidence interval of a forecast obtained via Holt's Linear Trend. Example and software are provided.
- [Mann-Whitney Simulation](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-simulation/): Describes how to use simulation to estimate the p-values of the Mann-Whitney test. This approach takes ties into account.
- [Logistic Regression](https://real-statistics.com/logistic-regression/): Tutorial on how to use and perform binary logistic regression in Excel, including how to calculate the regression coefficients using Solver or Newton's method.
- [Real Statistics Probit Capabilities](https://real-statistics.com/logistic-regression/probit-regression/real-statistics-probit-capabilities/): Describes the various Probit regression functions supported by the Real Statistics add-in, as well as the Probit data analysis tool for use in Excel.
- [Probit Regression](https://real-statistics.com/logistic-regression/probit-regression/): Describes probit regression and how to perform it in Excel. Examples and software are provided.
- [Logistic Regression Sample Size Tools](https://real-statistics.com/logistic-regression/logistic-regression-sample-size/logistic-regression-sample-size-tools/): Describes Real Statistics functions and data analysis tools that can be used to calculate the power and sample size for logistic regression in Excel.
- [Logistic Regression Sample Size (Binary)](https://real-statistics.com/logistic-regression/logistic-regression-sample-size/logistic-regression-sample-size-binary/): Describes how to estimate the minimum sample size required for logistic regression with a binary independent variable that is binomially distributed.
- [Logistic Regression Sample Size](https://real-statistics.com/logistic-regression/logistic-regression-sample-size/): Describes how to estimate the minimum sample size required for logistic regression with a continuous independent variable that is normally distributed.
- [Real Statistics Functions for Logistic Regression](https://real-statistics.com/logistic-regression/real-statistics-functions-logistic-regression/): Describes the functions provided in the Real Statistics Resource Pack (Excel add-in) to create binary Logistics Regression models in Excel.
- [Receiver Operating Characteristic (ROC) Curve](https://real-statistics.com/logistic-regression/receiver-operating-characteristic-roc-curve/): Brief tutorial on how to create the ROC curve for logistic regression in Excel. The Real Statistics add-in software calculates the ROC curve.
- [Classification Table](https://real-statistics.com/logistic-regression/classification-table/): Tutorial on the classification for logistic regression and software for calculating it in Excel. Includes accuracy, sensitivity, specificity, TPR, FPR and TNR.
- [Hosmer-Lemeshow Test](https://real-statistics.com/logistic-regression/hosmer-lemeshow-test/): Tutorial on how to perform the Hosmer-Lemeshow goodness of fit test for logistic regression in Excel using the Real Statistics Resource Pack.
- [Comparing Logistic Regression Models](https://real-statistics.com/logistic-regression/comparing-logistic-regression-models/): Comparing the base logistic model in Excel (with all the independent variables) with reduced and interaction models using the Real Statistics data analysis tool
- [Handling Categorical Data](https://real-statistics.com/logistic-regression/handling-categorical-data/): Describes how to code categorical data in Excel, especially for logistic regression by using Real Statistics' Extract Columns from a Data Range analysis tool.
- [Finding Logistic Regression Coefficients via Newton's Method](https://real-statistics.com/logistic-regression/finding-logistic-regression-coefficients-using-newtons-method/): How to use Newton's method in Excel to find the coefficients of the logistics regression model which best fits some given data. Focus is on binary logit model.
- [Testing the Fit of the Logistic Regression Model](https://real-statistics.com/logistic-regression/significance-testing-logistic-regression-model/): Describes various pseudo R-squared measures for logistic regression, including log-linear ratio, Cox and Snell, Nagelkerke.
- [Significance Testing of the Logistic Regression Coefficients](https://real-statistics.com/logistic-regression/significance-testing-logistic-regression-coefficients/): Describes how to test whether the logistic regression coefficients are significant using the Wald statistic and the chi-square test.
- [Finding Logistic Regression Coefficients using Excel’s Solver](https://real-statistics.com/logistic-regression/finding-logistic-regression-coefficients-using-excels-solver/): Describes how to use Excel's Solver tool to find the coefficients for the logistic regression model. A example is provided to show how this is done
- [Basic Concepts of Logistic Regression](https://real-statistics.com/logistic-regression/basic-concepts-logistic-regression/): How to perform logistic regression in Excel. Defines key concepts such as logit function, odds ratio and log.likelihood statistic.
- [Exponential Regression using Solver](https://real-statistics.com/regression/exponential-regression-models/exponential-regression-using-solver/): Describes how to use Excel's Solver to construct a nonlinear exponential regression model. Examples and software provided.
- [Exponential Regression using Newton's Method](https://real-statistics.com/regression/exponential-regression-models/exponential-regression-newtons-method/): Describes how to construct a nonlinear exponential regression model using Newton's Method. Examples and software provided.
- [Exponential Regression Newton's Method - Advanced](https://real-statistics.com/regression/exponential-regression-models/exponential-regression-newtons-method-advanced/): Provides the proofs of key properties associated with creating a nonlinear exponential regression model using Newton's Method
- [Real Statistics Exponential Regression Capabilities](https://real-statistics.com/regression/exponential-regression-models/real-statistics-exponential-regression-functions/): Describes the Real Statistics functions and data analysis tool that calculate the coefficients and predicted values for nonlinear exponential regression.
- [Exponential Regression using a Linear Model](https://real-statistics.com/regression/exponential-regression-models/exponential-regression/): How to perform exponential regression in Excel using built-in functions (LOGEST, GROWTH) and Excel's regression data analysis tool after a log transformation.
- [LOESS Regression using Excel](https://real-statistics.com/regression/loess-regression/loess-regression-using-excel/): Describes how to perform LOESS (aka LOWESS) regression in Excel. An example is given and explained and an Excel worksheet function is provided
- [LOESS Regression Data Analysis Tool](https://real-statistics.com/regression/loess-regression/loess-regression-data-analysis-tool/): Describes how to use Real Statistics' LOESS Regression data analysis tool to perform LOESS regression in Excel. Two examples are also provided.
- [Plots of Regression Confidence and Prediction Intervals](https://real-statistics.com/regression/confidence-and-prediction-intervals/plots-regression-confidence-prediction-intervals/): Shows how to create plots of the confidence and prediction intervals in Excel for a regression line. The sequence of steps is described and examples given
- [Regression Analysis - Advanced](https://real-statistics.com/regression/regression-analysis/regression-analysis-advanced/): Provides the proofs of key properties about Linear Regression Analysis.
- [Passing-Bablok Regression Support](https://real-statistics.com/regression/passing-bablok-regression/passing-bablok-regression-support/): Describes functions and data analysis tool used to conduct Passing-Bablok regression in Excel via the Real Statistics Resource Pack
- [Passing-Bablok Regression Linearity Assumption](https://real-statistics.com/regression/passing-bablok-regression/passing-bablok-regression-linearity-assumption/): Describes how to test whether or not the linearity assumption of Passing-Bablok regression is being met. A detailed Excel example is provided
- [Deming Regression Tool](https://real-statistics.com/regression/deming-regression/deming-regression-tool/): Describes how to create a Deming regression model in Excel using the Real Statistics software. Includes hypothesis testing.
- [Deming Regression Predictions](https://real-statistics.com/regression/deming-regression/deming-regression-predictions/): Describes how to make predictions using Deming regression in Excel, along with the prediction/confidence intervals. Examples and software are included.
- [Deming Regression Hypothesis Testing](https://real-statistics.com/regression/deming-regression/deming-regression-hypothesis-testing/): Describes how to conduct various hypothesis tests in Excel based on Deming regression. Examples and software are included.
- [Jackknifing for Deming Regression](https://real-statistics.com/regression/deming-regression/jackknifing/): Describes how to calculate the standard error of a parameter using jackknifing. Applies this technique to Deming regression. Examples and software are provided.
- [Deming Regression Basic Concepts](https://real-statistics.com/regression/deming-regression/deming-regression-basic-concepts/): Describes how to calculate the coefficients for Deming regression in Excel. Also shows how to test for normality of the data and generate residuals
- [LOESS Regression](https://real-statistics.com/regression/loess-regression/): Describes how to perform LOESS (aka LOWESS) regression. LOESS = locally estimated scatterplot smoothing and LOWESS = locally weighted scatterplot smoothing.
- [Passing-Bablok Regression](https://real-statistics.com/regression/passing-bablok-regression/): Tutorial on Passing-Bablok Regression, a non-parametric technique for comparing two methods. Includes Excel examples and software.
- [Deming Regression](https://real-statistics.com/regression/deming-regression/): Tutorial on Deming Regression using Excel. Includes numerous examples and a variety of worksheet functions as well as a data analysis tool.
- [Linear regression models for comparing means](https://real-statistics.com/regression/linear-regression-models-for-comparing-means/): How to use the techniques of regression to perform hypothesis testing of the mean (t-test). Also provides alternative effect size measure.
- [Power Regression](https://real-statistics.com/regression/power-regression/): Describes how to perform power regression in Excel using Excel's regression data analysis tool after a log-log transformation.
- [Exponential Regression Models](https://real-statistics.com/regression/exponential-regression-models/): Describes three models for performing exponential regression in Excel: linear and nonlinear. Software and examples are provided.
- [Confidence and prediction intervals for forecasted values](https://real-statistics.com/regression/confidence-and-prediction-intervals/): Defines the confidence interval and prediction interval for a simple linear regression and describes how to calculate these values in Excel.
- [Testing the significance of the slope of the regression line](https://real-statistics.com/regression/hypothesis-testing-significance-regression-line-slope/): How to test the significance of the slope of the regression line, in particular to test whether it is zero. Example of Excel's regression data analysis tool.
- [Fit of the Regression Line](https://real-statistics.com/regression/hypothesis-testing-regression-good-fit/): We show how to determine in Excel whether the linear regression line is a good fit for some data. We provide an example of how this is done in Excel.
- [Regression Analysis](https://real-statistics.com/regression/regression-analysis/): General principles of regression analysis, including the linear regression model, predicted values, residuals and standard error of the estimate.
- [Method of Least Squares](https://real-statistics.com/regression/least-squares-method/): How to apply the method of least squares in Excel to find the regression line which best fits a collection of data pairs.
- [Real Statistics Probability Functions](https://real-statistics.com/real-statistics-environment/real-statistics-probability-functions/): Provides lists of the Queueing, Markov Chain, and Hidden Markov Model worksheet functions supplied by the Real Statistics Resource Pack.
- [Estimating Markov Chain Parameters](https://real-statistics.com/probability-functions/markov-chains/estimating-markov-chain-parameters/): Describes how to estimate the transition matrix and initial distribution vector using a sequence of observed Markov chain states
- [Using Real Statistics Functions](https://real-statistics.com/real-statistics-environment/using-real-statistics-functions/): Describes how to obtain information about the worksheet functions provided by the Real Statistics Resource Pack. These functions augment Excel's capabilities.
- [M/M/1 Queueing Model with preemptive priority queueing](https://real-statistics.com/probability-functions/queueing-theory/m-m-1-preemptive-priority-queueing/): Describes the M/M/1 model with preemptive priority queueing and provides formulas for characteristics of this model, and explains how to calculate them in Excel
- [M/M/1 with non-preemptive priority queueing and variable service means](https://real-statistics.com/probability-functions/queueing-theory/m-m-s-non-preemptive-priority-queueing-variable-service/): Describes the M/M/1 non-preemptive priority queueing model with variable service, and shows how to calculate L, Lq, W, and Wq for each priority class in Excel.
- [M/M/s Queueing Model with pre-emptive priority queueing](https://real-statistics.com/probability-functions/queueing-theory/m-m-s-queueing-model-with-pre-emptive-priority-queueing/): Describes the M/M/s model with preemptive priority queueing and provides formulas for characteristics of this model, and explains how to calculate them in Excel
- [Multi-Server Queueing Simulation](https://real-statistics.com/probability-functions/queueing-theory/multi-server-queueing-simulation/): Describes how to construct a simulation of a queueing model with one or more servers. Provides an example in Excel as well as a worksheet function to do this.
- [Single Server Queueing Simulation](https://real-statistics.com/probability-functions/queueing-theory/single-server-queueing-simulation/): Describes how to construct a simulation of a queueing model with one server. Provides an example in Excel as well as a worksheet function to automate this.
- [M/D/1 Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-d-1-queueing-model/): Describes the M//1 queueing model and provides formulas for various characteristics of this model, and explains how to calculate them in Excel.
- [M/M/s/K Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-m-s-k-queueing-model/): Describes the M/M/s/K queueing model and provides formulas for various characteristics of this model, and explains how to calculate them in Excel.
- [M/M/1/K Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-m-1-k-queueing-model/): Describes the M/M/1/K queueing model and provides formulas for various characteristics of this model, and explains how to calculate them in Excel.
- [M/M/1 Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-m-1-queueing-model/): Describes the M/M/1 queueing model and provides formulas for various characteristics of this model, and explains how to calculate them in Excel.
- [M/M/s Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-m-s-queueing-model/): Describes the M/M/s queueing model and provides formulas for various characteristics of this model, and explains how to calculate them in Excel.
- [M/M/s/N Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-m-s-n-queueing-model/): Describes the M/M/s/N queueing model (finite population) and provides formulas for characteristics of this model, and explains how to calculate them in Excel.
- [Real Statistics Environment](https://real-statistics.com/real-statistics-environment/): Describes the Real Statistics user interface and provides an overview of the capabilities of the Real Statistics Excel-based software platform.
- [M/M/1/N Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-m-1-n-queueing-model/): Describes the M/M/1/N queueing model (finite population) and provides formulas for characteristics of this model, and explains how to calculate them in Excel.
- [Real Statistics Math Functions](https://real-statistics.com/real-statistics-environment/real-statistics-math-functions/): Provides a summary of various mathematical functions provided in the Real Statistics Resource Pack. These functions are not strictly statistical.
- [Converting a Decimal to a Fraction](https://real-statistics.com/other-mathematical-topics/rational-numbers/converting-decimal-to-fraction/): Describes how to convert a rational number in decimal form to a fraction. Includes examples and Excel worksheet functions for doing this.
- [Multivariate Regression Proofs](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-analysis-basic-concepts/multivariate-regression-proofs/): Provides proofs of basic properties about multivariate regression. Relates many of these to properties about multiple regression.
- [Brown-Forsythe F* Test for Two-way ANOVA](https://real-statistics.com/two-way-anova/two-factor-anova-with-replication/brown-forsythe-f-test-two-way-anova/): Brief description of the Brown-Forsythe F* Test for two-way analysis of variances (ANOVA). The focus is on the correct degrees of freedom.
- [Closest Color](https://real-statistics.com/real-statistics-environment/colors/closest-color/): Describes the distance between two color codes. Introduces the L*a*b* color coding, that more faithfully captures human visual perception. Incl. Excel examples.
- [Colors](https://real-statistics.com/real-statistics-environment/colors/): Describes how to test whether cells in an Excel sheet have a specified font or background (i.e. fill) color or are bold. Describes how to set the fill color.
- [Clusters based on Minkowski Distance](https://real-statistics.com/multivariate-statistics/cluster-analysis/real-statistics-k-means/clusters-minkowski-distance/): Describes how to perform k-means cluster analysis for non-Euclidean distance metrics (Minkowski distance) and for weighted distances.
- [Bayesian Binomial Testing Tools](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/bayesian-binomial-testing-tools/): Describes how to perform hypothesis testing for binomially distributed data in Excel using special software. Examples are provided.
- [PCA Support in Excel](https://real-statistics.com/multivariate-statistics/factor-analysis/principal-component-analysis/pca-support-in-excel/): How to perform Principal Component Analysis in Excel using the Real Statistics statistical analysis tool. Incl. data analysis tools and worksheet functions.
- [Random Walk Markov Chains](https://real-statistics.com/probability-functions/markov-chains/random-walk-markov-chains/): Defines the random walk Markov chain and describes several properties. Also describes Excel worksheet functions and gives some Excel examples.
- [Gambler's Ruin](https://real-statistics.com/probability-functions/markov-chains/gamblers-ruin/): Describes the gambler's ruin problem, and how to solve it using Markov chains and second-order difference equations. We also show how to solve it in Excel.
- [HMM Forward/Backward Algorithms](https://real-statistics.com/probability-functions/hidden-markov-models/hmm-forward-backward-algorithms/): Describes the forward and backward algorithms for Hidden Markov Models. Provides Excel examples and worksheet functions for doing this.
- [More second-order difference equations](https://real-statistics.com/other-mathematical-topics/first-order-difference-equations/more-second-order-difference-equations/): Describes how to solve second-order difference equations in Excel. Includes worksheet function descriptions and examples.
- [Baum-Welch Initialization](https://real-statistics.com/probability-functions/hidden-markov-models/baum-welch-initialization/): Describes a simple way to estimate the parameters of a Hidden Markov Model. We show how to use this approach to initialize the Baum-Welch algorithm.
- [Baum-Welch Worksheet Functions](https://real-statistics.com/probability-functions/hidden-markov-models/baum-welch-worksheet-functions/): Describes Excel worksheet functions in support of the Baum-Welch algorithm for Hidden Markov Models supplied by Real Statistics. Includes examples.
- [Viterbi Algorithm Worksheet Functions](https://real-statistics.com/probability-functions/hidden-markov-models/viterbi-algorithm-worksheet-functions/): Describes Excel worksheet functions in support of Viterbi's algorithm for Hidden Markov Models supplied by Real Statistics. Includes examples.
- [HMM Simulation](https://real-statistics.com/probability-functions/hidden-markov-models/hmm-simulation/): Describes how to create sequences of observations (and hidden states) from a Hidden Markov Model. Excel examples and worksheet functions are provided.
- [Hitting Probabilities Real Statistics Support](https://real-statistics.com/probability-functions/markov-chains/hitting-probabilities-real-statistics-support/): Describe Real Statistics support for Markov hitting probabilities and hit times. Includes Excel worksheet functions and examples.
- [Markov Chains Real Statistics Support](https://real-statistics.com/probability-functions/markov-chains/markov-chains-real-statistics-support/): Describes a data analysis tool and worksheet functions supplied by Real Statistucs to support Markov chains in Excel. Examples are included.
- [Real Statistics Resource Pack for Macintosh](https://real-statistics.com/free-download/real-statistics-resource-pack/real-statistics-resource-pack-macintosh/): How to download and install the Real Statistics Resource Pack containing new statistics function for use with Excel 2011, 2016, 2019, 365 for the Macintosh.
- [Real Statistics Resource Pack](https://real-statistics.com/free-download/real-statistics-resource-pack/): Provides access to a file containing the Real Statistics add-in for free download. Also, includes instructions on how to install the software.
- [Hitting Probabilities](https://real-statistics.com/probability-functions/markov-chains/hitting-probabilities/): Describes hitting and return probabilities in Markov chains and related topics. Includes gambler's ruin and random walks. Includes examples in Excel.
- [Hidden Markov Models](https://real-statistics.com/probability-functions/hidden-markov-models/): Describes what a hidden markov model (HMM) is and provides access to a series of topics about HMM, including Viterbi and Baum-Welch algorithms.
- [Power and Sample Size for Correlation Testing](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/power-sample-size-correlation-testing/): Describes how to determine the power and sample size requirements for one sample correlation testing in Excel. Includes examples and software.
- [HMM Baum-Welch Algorithm](https://real-statistics.com/probability-functions/hidden-markov-models/hmm-baum-welch-algorithm/): Describes the Baum-Welch algorithm to find the most likely set of parameters of an HMM that generates a sequence of observations. Includes Excel examples.
- [Viterbi Algorithm for HMM](https://real-statistics.com/probability-functions/hidden-markov-models/viterbi-algorithm-for-hmm/): Describes the Viterbi algorithm, that identifies a sequence of hidden states that generates a sequence of observations. Incl. Excel examples and functions.
- [Probability Functions](https://real-statistics.com/probability-functions/): Brief overview of concepts in probability theory that are useful in statistics, as well as basic concepts of discrete and continuous probability distributions.
- [Markov Chains](https://real-statistics.com/probability-functions/markov-chains/): Tutorial on discrete time Markov chains. We provide examples of how to solve problems based on Markov chains using Excel.
- [Log-linear Regression](https://real-statistics.com/log-linear-regression/): How to perform log-linear regression, where all variables are categorical. Provides a new way of modeling chi-squared goodness of fit and independence testing.
- [Two-way contingency tables](https://real-statistics.com/log-linear-regression/two-way-contingency-tables/): Re-examines two-way contingency tables studied in Independence Testing using a log-linear regression model.
- [Three-way contingency tables](https://real-statistics.com/log-linear-regression/three-way-contingency-tables/): How to determine in Excel the best fit log-linear model for data corresponding to three categorical variables. Uses iterative proportional fitting (IPFP).
- [Non-comprehensive models](https://real-statistics.com/log-linear-regression/three-way-contingency-tables/non-comprehensive-model/): How to determine in Excel how good a fit various non-comprehensive log-linear regression models are for data represented in a three-way contingency table.
- [Mutual independence model](https://real-statistics.com/log-linear-regression/three-way-contingency-tables/mutual-independence-model/): How to determine in Excel how good a fit a mutual independence log-linear regression model is for data represented in a three-way contingency table.
- [Partial independence model](https://real-statistics.com/log-linear-regression/three-way-contingency-tables/partial-independence-model/): How to determine in Excel how good a fit a partial independence log-linear regression model is for data represented in a three-way contingency table.
- [Conditional independence model](https://real-statistics.com/log-linear-regression/three-way-contingency-tables/conditional-independence-model/): How to determine in Excel how good a fit a conditional independence log-linear regression model is for data represented in a three-way contingency table.
- [Saturated model for three-way contingency tables](https://real-statistics.com/log-linear-regression/three-way-contingency-tables/saturated-model-three-way-contingency-tables/): This webpage provides basic information about the saturated model for three-way contingency tables for log-linear regression.
- [Summary of models for two-way contingency tables](https://real-statistics.com/log-linear-regression/two-way-contingency-tables/summary-of-models-two-way-contingency-tables/): This webpage reviews all the log-linear regression models with up to two variables (two-way contingency tables) to find the best fit.
- [Other models for two-way contingency tables](https://real-statistics.com/log-linear-regression/two-way-contingency-tables/other-models-two-way-contingency-tables/): Log-linear regression models for two-way contingency tables where at least one variable is missing: equiprobability and conditional equiprobability models.
- [Independence model for two-way contingency tables](https://real-statistics.com/log-linear-regression/two-way-contingency-tables/independence-model-two-way-contingency-tables/): Describes the log-linear regression approach to independence testing for two-way contingency tables and the relationship to chi-square independence testing.
- [Saturated model for two-way contingency tables](https://real-statistics.com/log-linear-regression/two-way-contingency-tables/saturated-model-two-way-contingency-tables/): Describes the saturated model for two-way contingency tables in log-linear regression. Includes the concepts of marginal average and marginal totals.
- [Gibbs Sampler Two Sample Binomial](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/gibbs-sampler-two-sample-binomial/): Describes how to apply Gibbs Sampler to the two independent, binomially distributed samples case. Excel examples and software are included.
- [Two Sample Binomial Metropolis Algorithm](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/two-sample-binomial-metropolis/): Shows how to apply the Metropolis algorithm to the case where there are two independent, binomially distributed samples. Excel example and software are included
- [Effective Sample Size for Metropolis Algorithm](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/markov-chain-monte-carlo/ess-metropolis-algorithm/): Describes how to calculate the effective sample size (ESS) for the Metropolis algorithm using a binomial data example in Excel.
- [Bayesian Beta Test Sample and Effect Sizes](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/bayesian-beta-sample-and-effect-sizes/): Determine the beta effect size needed to achieve a given level of support for a hypothesis for a given sample size. Also find the sample size needed in Excel.
- [Bayesian Characterization of a Beta Distribution](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/bayesian-characterization-of-a-beta-distribution/): Describes how to estimate the mean, median, mode, HDI, equal-tailed CI, and Bayesian Factor for Bayesian analysis in Excel based on a beta distribution.
- [Bayesian Binomial Hypothesis Testing](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/bayesian-binomial-hypothesis-testing/): Describes how to conduct hypothesis testing for binomially distributed data using a Bayesian approach. Provides examples in Excel.
- [High Density Interval (HDI)](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/high-density-interval-hdi/): Describes how to calculate a high-density interval (HDI) in Excel for a conjugate beta distribution when the data follow a binomial distribution
- [Bayesian Analysis using Grids](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-grid-approximation/bayesian-analysis-using-grids/): Describes how to estimate the mean, median, mode, HDI, equal-tailed CI, and Bayesian Factor for Bayesian analysis in Excel based on a grid.
- [Bayesian Grid Approximation](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-grid-approximation/): Describes how to construct a grid in Bayesian analysis for binomially distributed data using triangular distribution priors. Includes Excel examples
- [Credible Interval and HDI](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-grid-approximation/credible-interval-hdi/): Defines a credible interval and the high-density interval (HDI) and shows how to calculate an HDI in Excel from a Bayesian grid
- [Creating a Grid using Real Statistics](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-grid-approximation/creating-grid-using-real-statistics/): Describes how to create a grid for Bayesian analysis in Excel using a Real Statistics data analysis tool. Includes an example and software
- [Bayesian Mixed Model Contrasts](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-contrasts/bayesian-mixed-model-contrasts/): How to create contrasts for models with both between-subjects and within-subjects factors. Provides Bayesian analysis examples in Excel and Excel functions.
- [Bayesian Mann-Whitney Support](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-mann-whitney-test/bayes-mann-whitney-support/): Provides an example of how to perform the Bayesian Mann-Whitney test in Excel, using both the small and large sample methods. Also provides worksheet functions.
- [More Bayesian Non-parametric Tests](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/more-bayesian-non-parametric-tests/): Describes how to perform the Bayesian versions of the McNemar, Sign, and Median tests in Excel. Examples and Excel worksheet functions are provided.
- [Bayesian Gamma Test](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-gamma-test/): How to conduct a non-parametric Gamma correlation test using a Bayesian approach in Excel. Provides worksheet functions, data analysis tool and examples.
- [Bayesian Kendall’s Tau Test](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-kendalls-tau/): How to conduct a non-parametric Kendall's tau correlation test using a Bayesian approach in Excel. Provides worksheet functions, data analysis tool & examples.
- [Bayesian Contrasts](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-contrasts/): How to extend the Bayesian versions of the Signed Ranks and Mann-Whitney non-parametric tests using contrasts. Provides examples in Excel and Excel functions.
- [Bayesian Mann-Whitney Test](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-mann-whitney-test/): Describes the Bayesian version of the Mann-Whitney non-parametric test for two independent samples. Provides examples in Excel and Excel tools.
- [Bayesian Signed Ranks Test](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-signed-ranks-test/): Describes the Bayesian version of the Wilcoxon Signed-Ranks non-parametric test. Provides examples in Excel and Excel tools.
- [Bayesian Signed-Rank Test Support](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-signed-ranks-test/bayesian-signed-rank-test-support/): Describes various Excel worksheet functions to perform the Bayesian version of the Wilcoxon Signed-Ranks non-parametric test. Also explains a data analysis tool
- [Jeffreys' Priors](https://real-statistics.com/bayesian-statistics/non-informative-priors/jeffreys-priors/): Describes what a Jeffreys' prior is and what are the Jeffreys' priors for binomially distributed and normally distributed data.
- [Bayesian Hypothesis Testing for Normal Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/): Describes how to perform hypothesis testing for normally distributed data using a Bayesian approach. Here we describe one-sided tests.
- [Bayesian Non-parametric Testing](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/): Tutorial on Bayesian non-parametric testing. Includes the Wilcoxon Signed-Ranks and Mann-Whitney tests. Provides examples in Excel and Excel tools.
- [Bayesian Independence Testing](https://real-statistics.com/bayesian-statistics/bayesian-independence-testing/): How to determine whether the two variables defined in a contingency table are independent using a Bayesian approach. Incl. Excel examples & worksheet functions
- [Bayesian Correlation Testing](https://real-statistics.com/bayesian-statistics/bayesian-correlation-testing/): Describes how to conduct a correlation hypothesis test using a Bayesian approach in Excel. Worksheet functions, data analysis tools and examples are provided.
- [Non-informative Priors](https://real-statistics.com/bayesian-statistics/non-informative-priors/): Provides a description on non-informative priors, including improper priors and Jefferies priors. These are used when we don't have useful prior information.
- [Bayesian Statistics for Binomial Distributed Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/): Tutorial on Bayesian Statistics in the context of data that has a binomial distribution: beta conjugate priors, grids, MCMC. Includes Excel examples & software
- [Bayesian Statistics Introduction](https://real-statistics.com/bayesian-statistics/bayesian-statistics-introduction/): Provides a brief introduction to Bayesian statistics, focusing on the differences from classical, frequentist statistics.
- [Bayesian Hypothesis Testing](https://real-statistics.com/bayesian-statistics/bayesian-statistics-introduction/bayesian-hypothesis-testing/): Describes how to perform hypothesis testing in the Bayes context. Also describes the Bayes Factor and provides an example of hypothesis testing.
- [Bayesian Example](https://real-statistics.com/bayesian-statistics/bayesian-statistics-introduction/bayesian-example/): Describes a simple example of the Bayesian approach to determining the probability that someone has a disease based on the results of a test for the disease.
- [Kaplan-Meier Theory](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/kaplan-meier-theory/): Provides some of the mathematical basis for the Kaplan-Meier procedure, especially the proofs of some of the properties. Requires calculus background.
- [Real Statistics Capabilities for Kaplan-Meier](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/real-statistics-kaplan-meier/): Describes how to perform Kaplan-Meier survival analysis in Excel, as well as the logrank test. Excel examples are provided as well as Excel tools.
- [Hazard Ratio](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/hazard-ratio/): Describes how to calculate the hazard ratio for two samples based on the Kaplan-Meier procedure. Examples are provided in Excel.
- [Alternative Kaplan-Meier Comparison Tests](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/kaplan-meier-comparison-tests/): Describes how to test whether two samples have significantly different survival distributions. Includes example and Excel software.
- [Log-Rank Test](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/log-rank-test/): Describes how to calculate the log-rank test in Excel to compare the survival rates of two samples using the Kaplan-Meier procedure. Examples and Excel software
- [Hazard Function](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/hazard-function/): Describes how to calculate the hazard function and cumulative hazard function for Kapan-Meier. We also describe the standard error of the hazard function.
- [Confidence Interval for the Survival Function](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/confidence-interval-for-the-survival-function/): Describes how to calculate the standard error and confidence intervals for the survival function S(t) from Kaplan-Meier. Includes examples and Excel software.
- [Survival Curve](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/survival-curve/): Describes how to create a step chart in Excel containing the survival curve for S(t) from the Kaplan-Meier procedure. Provides an example.
- [Kaplan-Meier Overview](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/kaplan-meier-overview/): Describes the basic ideas behind the Kaplan-Meier non-parametric approach to Survival Analysis. Includes an example in Excel
- [Cox Regression Theory](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-theory/): Provides some of the mathematical basis for Cox Regression, especially the proofs of some of the properties. Requires calculus background.
- [Cox Regression Residuals](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-residuals/): Describes the various types of residuals that can be used with Cox Regression to identify potential outliers and test the proportional hazards assumption.
- [Estimating the Baseline Hazard Function](https://real-statistics.com/survival-analysis/cox-regression/baseline-hazard-function/): Describes how to estimate the baseline hazard function (as well as the cumulative baseline hazard function and survival function) for Cox Regression.
- [Cox Regression Models with Multiple Deaths per Time Period](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-models-ties/): Describes how to deal with multiple deaths in time intervals in Cox Regression, incl. Breslow and Efron estimates. Includes examples and Excel software.
- [Determining the Fit of a Cox Regression Model](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-model-fit/): Describes how to determine the goodness-of-fit of a Cox regression model using chi-square. Examples and Excel software are included.
- [Cox Regression using Newton's Method](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-using-newtons-method/): Describes how to perform Cox proportional hazard method (Cox's regression) in Excel. Includes examples and Excel add-in software.
- [Cox Regression using Solver](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-solver/): Describes how to perform Cox's proportional hazard model (Cox's regression) in Excel using Solver. Examples and Excel software are included.
- [Cox Regression Basic Concepts](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-basic-concepts/): Describes the basic concepts of Cox Proportional Hazard Regression, including concepts such as hazard ratio and relative risk.
- [Cox Regression](https://real-statistics.com/survival-analysis/cox-regression/): Describes how to create a Cox proportional hazards model (Cox Regression). In Excel. Examples and Excel software are included.
- [Kaplan-Meier Survival Analysis](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/): Describes how to perform the Kaplan-Meier procedure in Excel, including survival curves and log-rank test. Includes examples and Excel software.
- [Basic Concepts of Survival Analysis](https://real-statistics.com/survival-analysis/survival-analysis-basic-concepts/): Describes the main concepts in Survival Analysis, including censoring (left, right, interval), survivor function, and hazard function.
- [Survival Analysis](https://real-statistics.com/survival-analysis/): Describes how to perform Survival Analysis with censored data. Includes examples and Excel software. Topics: Cox Regression and Kaplana-Meier.
- [Chi-square Goodness of Fit Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/chi-square-goodness-of-fit-test/): Describes how to conduct the Chi-square Goodness of Fit Test in Excel. A detailed example and an Excel worksheet function are provided.
- [Two-Sample Anderson-Darling Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/two-sample-anderson-darling-test/): Describes how to perform a two-sample Anderson-Darling test to determine whether two data sets come from the same distribution. Examples & software provided.
- [Two-Sample Kolmogorov-Smirnov Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/two-sample-kolmogorov-smirnov-test/): Describes how to apply the Two Sample Kolmogorov-Smirnov Test to determine if two samples have the same distribution. Examples and Excel add-in software.
- [One-Sample Kolmogorov-Smirnov Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/one-sample-kolmogorov-smirnov-test/): Describes how to use the One Sample Kolmogorov-Smirnov Test to determine whether sample data follows a specific distribution; examples, Excel add-in software.
- [Goodness of Fit Tests](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/): Tutorial on goodness-of-fit tests, incl. the chi-square test, Kolmogorov-Smirnov test, & the Anderson-Darling test. Incl. numerous Excel functions and examples.
- [Permutation Test for Paired Samples](https://real-statistics.com/non-parametric-tests/permutation-test-for-paired-samples/): Describes the permutation non-parametric test for paired samples and explains how to calculate and perform it in Excel. Incl. examples and Excel functions.
- [Fligner-Policello Test](https://real-statistics.com/non-parametric-tests/fligner-policello-test/): Describes how to perform the nonparametric Fligner-Policello Test in Excel to determine whether two population medians are equal. An example is provided.
- [Runs Up/Down Test](https://real-statistics.com/non-parametric-tests/one-sample-runs-test/runs-up-down-test/): Describes how to perform a one-sample runs up/down test in Excel. Examples are provided as well as a new Excel worksheet function.
- [One-Sample Runs Test](https://real-statistics.com/non-parametric-tests/one-sample-runs-test/): Describes several methods for performing a one-sample runs test in Excel. Examples are provided as well as new Excel worksheet functions.
- [Siegel-Tukey Test for Equal Variability](https://real-statistics.com/non-parametric-tests/siegel-tukey-test-for-equal-variability/): Describes the Siegel-Tukey test of equal variability and explains how to implement it in Excel. Examples and Excel worksheet functions are provided.
- [Moses' Test for Equal Variability](https://real-statistics.com/non-parametric-tests/moses-test-for-equal-variability/): Describes Moses' test for equal variability and explains how to calculate and test it in Excel. Examples and Excel worksheet functions are provided.
- [Data Analysis Tools for Non-parametric Tests](https://real-statistics.com/non-parametric-tests/data-analysis-tools-non-parametric-tests/): Describes how to use a data analysis tool provided in the Real Statistics Resource Pack to perform non-parametric tests in Excel. Software and examples given.
- [Resampling Data Analysis Tool](https://real-statistics.com/non-parametric-tests/resampling-data-analysis-tool/): Describes how to use a data analysis tool provided in the Real Statistics Resource Pack to perform resampling tests in Excel. Software and examples given.
- [Standard Error of Gini Index](https://real-statistics.com/non-parametric-tests/gini-coefficient/standard-error-of-gini-index/): Describes how to calculate the standard error of the Gini coefficient using bootstrapping, and how to use this to create a confidence interval.
- [Real Statistics Support for Tolerance Intervals](https://real-statistics.com/non-parametric-tests/non-parametric-tolerance-interval/real-statistics-support-for-tolerance-intervals/): Describes Real Statistics functions that can be used to create tolerance intervals for both normally distributed and non-normally distributed data in Excel.
- [Non-parametric Tolerance Interval](https://real-statistics.com/non-parametric-tests/non-parametric-tolerance-interval/): Tutorial on how to create a non-parametric tolerance interval in Excel for data that is not normally distributed. An example is also provided.
- [Signed-Ranks Test Power and Sample Size](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/signed-ranks-power/): Describes how to calculate the power or sample size for a Wilcoxon Signed-Ranks test using simulation or estimated from the power of a t test.
- [Signed-Ranks Median Confidence Interval](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/signed-ranks-median-confidence-interval/): Describes how to calculate the confidence interval of the median based on the Wilcoxon signed/ranks test. Examples given in Excel.
- [Signed-Ranks Simulation](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/signed-ranks-simulation/): Describes how to use simulation to estimate the p-values of the Wilcoxon Signed-ranks test. This approach takes ties into account.
- [Signed Ranks Exact Test](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/wilcoxon-signed-ranks-exact-test/): Describes how to construct the Wilcoxon Signed Ranks Exact Test usin the permutation distribution in Excel. Software and examples provided.
- [Wilcoxon Signed-Ranks Test – Advanced](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/wilcoxon-signed-ranks-test-advanced/): Proof of Property 1 of Wilcoxon Signed-Ranks Test.showing that the test statistic is approximately normally distributed.
- [Wilcoxon Signed-Ranks Test](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/): How to perform the Wilcoxon signed ranks test in Excel for a single sample and for paired samples. Includes using a table of critical values or normal approx.
- [Permutation Test for Two Independent Samples](https://real-statistics.com/non-parametric-tests/permutation-test-for-two-independent-samples/): Describes the two independent samples permutation non-parametric test and explains how to calculate and perform it in Excel. Incl. examples and Excel functions.
- [Mann-Whitney Test - Proofs](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-test-advanced/): This webpage provides proofs of Properties 1 and 2 for the Mann-Whitney Test. These are used to justify the normal approximation.
- [Mann-Whitney Power](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-power/): Describes how to calculate the power or sample size for a Mann-Whitney test using simulation or estimated from the power of a t test.
- [Mann-Whitney Median Confidence Interval](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-median-confidence-interval/): Describes how to calculate the confidence interval of the median based on the Mann-Whitney test. Examples given in Excel.
- [Mann-Whitney Exact Test](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-exact-test/): Describes how to calculate the Mann-Whitney test using the permutation distribution to get exact values. Software and examples included.
- [Mann-Whitney Test for Independent Samples](https://real-statistics.com/non-parametric-tests/mann-whitney-test/): How to perform a Mann-Whitney non-parametric test for independent samples in Excel when the assumptions for the t-test are not met.
- [Wilcoxon Rank Sum Test - Proofs](https://real-statistics.com/non-parametric-tests/wilcoxon-rank-sum-test/wilcoxon-rank-sum-test-advanced/): Presents the proofs of Wilcoxon Rank Sum Test properties 1 and 2, which show how to calculate the mean and standard deviation.
- [Wilcoxon Rank Sum Exact Test](https://real-statistics.com/non-parametric-tests/wilcoxon-rank-sum-test/wilcoxon-rank-sum-exact-test/): Describes how to perform an exact test version of Wilcoxon's Rank-Sum test for independence in Excel. Software and examples included.
- [Wilcoxon Rank Sum Test for Independent Samples](https://real-statistics.com/non-parametric-tests/wilcoxon-rank-sum-test/): How to perform the Wilcoxon ranked sum non-parametric test for independent samples in Excel, a test used when the assumptions for the t test are violated.
- [Brunner-Munzel Data Analysis Tool](https://real-statistics.com/non-parametric-tests/brunner-munzel-test/brunner-munzel-data-analysis-tool/): Describes how to conduct the Brunner-Munzel Test or Permutation Brunner-Munzel Test in Excel using the Real Statistics data analysis tool.
- [Permutation Brunner-Munzel Test](https://real-statistics.com/non-parametric-tests/brunner-munzel-test/permutation-brunner-munzel-test/): Describes how to use the (random) permutation version of the Brunner-Munzel test to compare two independent samples. Provides an example and Excel function.
- [Brunner-Munzel Test Example](https://real-statistics.com/non-parametric-tests/brunner-munzel-test/brunner-munzel-test-example/): Provides an example of how to conduct the Brunner-Munzel test for stochastic equality in Excel. Also includes an Excel worksheet function to carry out the test
- [Brunner-Munzel Test](https://real-statistics.com/non-parametric-tests/brunner-munzel-test/): Provides an overview of the Brunner-Munzel test for two independent samples, especially when the samples have unequal variances.
- [Mood's Median Test (for two samples)](https://real-statistics.com/non-parametric-tests/moods-median-test-two-samples/): Describes how to apply the Mood's Median non-parametric test in Excel for two samples. Includes an example and Excel functions to calculate the results.
- [Trinomial Test](https://real-statistics.com/non-parametric-tests/trinomial-test/): Describes how to conduct the trinomial test, a non-parametric test similar to the sign test but with more power, in Excel. Example and software are provided.
- [Introduction to Non-parametric Tests](https://real-statistics.com/non-parametric-tests/introduction-non-parametric-tests/): Provides an overview of when non-parametric tests are used, as well as the advantages and shortcomings of using non-parametric tests.
- [Non-parametric Tests](https://real-statistics.com/non-parametric-tests/): Tutorial on how to perform a variety of non-parametric statistical tests in Excel when the assumptions for a parametric test are not met.
- [FIML Real Statistics Data Analysis Tool](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/fiml-real-statistics-data-analysis-tool/): Describes the Real Statistics Full Information Maximum Likelihood (FIML) data analysis tool for calculating multiple regression with missing data using FIML.
- [Multiple Regression using FIML](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/multiple-regression-using-fiml/): Detailed description and example of how to create a multiple regression analysis in Excel even when there is missing data by using the FIML procedure.
- [Adding constraints to Solver for FIML](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/fiml-using-solver/adding-constraints-solver-fiml/): Describes how to add constraints to the Solver approach to finding a Full Information Maximum Likelihood (FIML) solution to missing data.
- [FIML using Solver](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/fiml-using-solver/): Description of how to use Excel's Solver to deal with missing data by means of the FIML procedure. Examples and add-in software are provided.
- [Initialization of FIML](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/initialization-fiml/): Description of how to set up Excel to carry out the FIML procedure for dealing with missing data using Solver. Examples and software are provided.
- [FIML Basic Concepts](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/fiml-basic-concepts/): Brief overview of the objectives of the FIML procedure for dealing with missing data and the basic theoretical basic for the approach.
- [Full Information Maximum Likelihood (FIML)](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/): Tutorial on how to use the Full Information Maximum Likelihood (FIML) methodology for dealing with missing data in Excel. Includes examples and software.
- [Multiple Regression with Missing Data](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/multiple-regression-missing-data/): Describes how to carry out multiple regression in Excel when some of the data is missing. Gives an example and provides an add-in software to do this.
- [Number of Imputations](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/number-of-imputations/): A brief explanation of the recommended number of multiple imputations required to achieve a stated level of efficiency when performing multiple imputation.
- [One Complete Imputation using FCS](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/one-complete-imputation-using-fcs/): Detailed description of how to perform one imputation using FCS/MICE in Excel, including an example. Also explanation of free software support.
- [One Step of the FCS Procedure](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/fcs-procedure-one-step/): Provides a detailed description of one step in the FCS/MICE procedure for performing multiple imputation. Provides examples and a worksheet function in Excel.
- [Frequency and Patterns of Missing Data](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/missing-data-frequency-patterns/): Description of frequency and patterns of missing data and how to generate reports of these in Excel using functions from the Real Statistics Resource Pack.
- [Fully Conditional Specification (FCS)](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/fully-conditional-specification-fcs/): Provides an overview of the fully conditional specification (FCS) approach, also called the multivariate imputation by chained equations (MICE).
- [Multiple Imputation Overview](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/multiple-imputation-overview/): A brief overview of the multiple imputation approach for dealing with missing data. The basic concepts are described and followed up in subsequent webpages.
- [Traditional Approaches for Handling Missing Data](https://real-statistics.com/handling-missing-data/traditional-approaches-handling-missing-data/): Tutorial on traditional approaches for dealing with missing data, incl. listwise deletion and single imputation (regression, stochastic regression, etc.).
- [Contingency tables with missing elements](https://real-statistics.com/handling-missing-data/em-algorithm/contingency-tables-with-missing-elements/): Describes how to deal with contingency tables with missing data. Missing data is imputed using an EM algorithm. Excel examples and software is included.
- [EM Missing Multivariate Normal Data Tools](https://real-statistics.com/handling-missing-data/em-algorithm/em-missing-multivariate-normal-data-tools/): Describes how to use Real Statistics functions and data analysis tool to implement the EM algorithm for Missing Multivariate Normal Data in Excel.
- [EM algorithm multiple patterns of missing data](https://real-statistics.com/handling-missing-data/em-algorithm/em-algorithm-multiple-missing-data-patterns/): Describes how to impute missing data and estimate the parameters for multivariate normally distributed data with multiple missing data patterns in Excel.
- [EM multivariate normal with missing data](https://real-statistics.com/handling-missing-data/em-algorithm/em-multivariate-normal-with-missing-data/): Describes how to use the EM algorithm in Excel to impute missing data elements for data that follows a multivariate normal distribution.
- [Multivariate Normal Properties](https://real-statistics.com/handling-missing-data/em-algorithm/multivariate-normal-properties/): Describes various properties of multivariate normally distributed data that are useful in performing the EM algorithm when there is missing data.
- [Types of Missing Data](https://real-statistics.com/handling-missing-data/types-of-missing-data/): Describes the types of missing data: missing completely at random (MCAR), missing at random (MAR) and not missing at random
- [Multi-sample Correlation Test Support](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/multi-sample-correlation-test-support/): Describes how to conduct hypothesis testing for 3 or more correlations in Excel. Includes Tukey HSD & Dunnett's post hoc tests, plus contrasts.
- [Correlation Testing for more than two samples](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/correlation-testing-more-than-two-samples/): Describes how to conduct hypothesis testing for 3 or more correlations. Includes Tukey HSD & Dunnett's post hoc tests, plus contrasts. Includes Excel examples.
- [Power and Sample Size for Two-Sample Correlation Testing](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/power-and-sample-size-for-two-sample-correlation-testing/): Describes how to calculate the power of a two-sample correlation test in Excel as well as the minimum sample size. Excel examples and functions are provided.
- [Comparing correlation coefficients of non-overlapping dependent samples](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/correlations-non-overlapping-dependent-samples/): How to perform hypothesis testing in Excel to determine whether the correlation coefficients of 2 non-overlapping dependent samples are significantly different.
- [Comparing correlation coefficients of overlapping samples](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/comparing-correlation-coefficients-two-dependent-samples/): How to perform hypothesis testing in Excel to determine whether the correlation coefficients of two overlapping dependent samples are significantly different.
- [Two Sample Hypothesis Testing for Correlation](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/): How to perform hypothesis testing in Excel to determine whether the correlation coefficients of two independent samples are significantly different.
- [Correlation Testing via Exact Test](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/correlation-testing-via-exact-test/): Describes the distribution of the correlation coefficient and hypothesis testing using this distribution. Includes examples and software.
- [Correlation testing via Fisher transformation](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/correlation-testing-via-fisher-transformation/): How to perform one sample correlation hypothesis testing in Excel using the Fisher transformation; includes examples and software.
- [Correlation testing via t test](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/correlation-testing-via-t-test/): Describes how to perform a one-sample correlation test using the t-test in Excel. Includes examples and software. Also provides Excel functions for the test.
- [One Sample Hypothesis Testing for Correlation](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/): How to perform one sample correlation hypothesis testing in Excel using t test or Fisher transformation; includes examples, sample size and power calculation.
- [Correlation as t-test proofs](https://real-statistics.com/correlation/dichotomous-variables-t-test/correlation-as-t-test-proofs/): Provides proofs of properties linking correlations and t-tests. Includes properties about the point-biserial correlation and r-effect size
- [Box-Cox Normal Transformation](https://real-statistics.com/correlation/box-cox-transformation/box-cox-normal-transformation/): Describes how to calculate the value of lambda in Excel (using Goal Seek) which creates the best Box-Cox normal transformation. Includes software and examples.
- [Box-Cox Linear Transformation](https://real-statistics.com/correlation/box-cox-transformation/box-cox-linear-transformation/): Describes how to choose a value for lambda in Excel which optimizes the Box-Cox linear transformation. Shows how to do this using Goal Seek. Also examples given
- [Box-Cox Transformation Options](https://real-statistics.com/correlation/box-cox-transformation/box-cox-transformation-options/): Describes more Box-Cox transformation features (incl. Hawkins-Weisberg) and a data analysis tool and Excel worksheet functions to support such transformations
- [Polychoric Correlation Tool](https://real-statistics.com/correlation/polychoric-correlation/polychoric-correlation-tool/): Describes the Real Statistics Polychoric Correlation data analysis tool and various Excel worksheet functions in support of the polychoric correlation.
- [Polychoric Correlation using Solver](https://real-statistics.com/correlation/polychoric-correlation/polychoric-correlation-using-solver/): Describes how to calculate the polychoric correlation coefficient using Excel Solver. Examples and software are provided.
- [Polychoric Correlation Basic Concepts](https://real-statistics.com/correlation/polychoric-correlation/polychoric-correlation-basic-concepts/): Describes the basic ideas underlying the polychoric correlation, including the tetrachoric correlation coefficient. These correlations are compared to Pearson's
- [Lambda Coefficient](https://real-statistics.com/correlation/lambda-coefficient/): Describes the lambda (asymmetric) measure of association and explains how to calculate and test it in Excel. Examples & Excel worksheet functions are provided.
- [Ordered Chi-square Test of Independence](https://real-statistics.com/correlation/ordered-chi-square-independence-test/): Tutorial on how to conduct the chi-square test for independence when the rows and columns are ordered. Examples and software in Excel are included.
- [Polychoric Correlation](https://real-statistics.com/correlation/polychoric-correlation/): Tutorial on polychoric correlation (including tetrachoric correlation) and how to calculate them in Excel. Examples and software are included.
- [Box-Cox Transformation](https://real-statistics.com/correlation/box-cox-transformation/): Describes how to perform the Box-Cox transformations in Excel to create a transformation to normality. Finds optimal transformation. Software and examples.
- [Biserial Correlation](https://real-statistics.com/correlation/biserial-correlation/): Shows how to calculate the biserial correlation coefficient in Excel, as well as the p-value and confidence interval. Example included.
- [Resampling for Correlation](https://real-statistics.com/correlation/resampling-correlation/): Describing how to perform resampling (bootstrapping, randomization) for correlation testing and confidence interval. Examples and software are included.
- [Multiple Correlation](https://real-statistics.com/correlation/multiple-correlation/): Shows how to calculate various measures of multiple correlation coefficient. Also reviews Excel's Correlation data analysis tool.
- [Correlation and Association](https://real-statistics.com/correlation/): We explore the concept of correlation (especially using Pearson's correlation coefficient) and how to perform one and two sample hypothesis testing
- [Neural Network to Recognize Digits](https://real-statistics.com/neural-networks/neural-network-to-recognize-digits/): Describes how to build, training, and test a neural network that recognizes hand-written digits from 0 to 9 in Excel using Real Statistics capabilities
- [Neural Network Analysis Tools](https://real-statistics.com/neural-networks/neural-network-analysis-tools/): Describes how to use the Real Statistics Training a Neural Network data analysis tool to train the XOR neural network in Excel.
- [Simple Neural Network Example](https://real-statistics.com/neural-networks/simple-neural-network-example/): Provides an example of how to use an Excel spreadsheet to train a simple neural network to replicate an XOR gate. All formulas are explained.
- [Training and Testing Methodology](https://real-statistics.com/neural-networks/training-and-testing-methodology/): We describe the approach used for testing a neural network, using backward propagation, as well as testing the accuracy of the neural network
- [Training a Neural Network](https://real-statistics.com/neural-networks/training-a-neural-network/): We now describe how to train a neural network. Emphasis is placed on how backward propagation is performed using a set of training data.
- [Neural Networks Basic Concepts](https://real-statistics.com/neural-networks/neural-networks-basic-concepts/): Describes the general concepts of a neural network. Describes how a neural network functions, including forward propagation and backward propagation.
- [Neural Networks](https://real-statistics.com/neural-networks/): Tutorial on (artificial) neural networks, including implementations in Excel. Also includes several examples using Excel capabilities.
- [Coarsened Exact Matching](https://real-statistics.com/matching/coarsened-exact-matching/): Describes how to use coarsened exact matcthng (CEM) to match confounding effects in treatment and control groups. Includes Excel examples and software.
- [Propensity Score Matching](https://real-statistics.com/matching/propensity-score-matching/): Describes how to use propensity score matching (PSM) to match confounding effects in treatment and control groups. Includes Excel examples and software.
- [Matching](https://real-statistics.com/matching/): Tutorial on statistical matching techniques with a focus on propensity score matching (PSM) and coarsened exact matching. Examples & software in Excel provided.
- [Hausman Test](https://real-statistics.com/panel-data-models/hausman-test/): Describes how to use Hausman's test to determine if a fixed-effects or random-effects model is a better fit for your panel data. Incl. Excel function & example.
- [Polytomous Model Tools](https://real-statistics.com/reliability/item-response-theory/polytomous-model-tools/): Describes how to use Real Statistics functions and a data analysis tool to build and analyze the fit of a polytomous Rasch model using the UCON method in Excel.
- [Polytomous Model Fit](https://real-statistics.com/reliability/item-response-theory/polytomous-model-fit/): Describes how to test the fit of a polytomous UCON Rasch model in Excel. Includes how to calculate the infit and outfit values.
- [Building a Polytomous Model](https://real-statistics.com/reliability/item-response-theory/building-a-polytomous-model/): Describes how to manually construct a polytomous Rasch model using the UCON method. How this is done is demonstrated via a step-by-step example in Excel.
- [Polytomous Model Basic Concepts](https://real-statistics.com/reliability/item-response-theory/polytomous-model-basic-concepts/): Describes the basic concepts of the UCON method of Rasch analysis for polytomous data (i.e. scores 0, 1, 2, …, m where m > 0). Key formulas are described.
- [Ability and Difficulty Measurements](https://real-statistics.com/reliability/item-response-theory/ability-difficulty-measurements/): Provides an expanded definition of subject ability and item difficulty for Rasch IRT models, especially with Likert scores and non-dichotomous scoring.
- [Support for PROX Method](https://real-statistics.com/reliability/item-response-theory/prox-method-support/): Describes how to build a Rasch model (using the PROX method) in Excel using the Real Statistics statistical analysis software.
- [PROX Model Example](https://real-statistics.com/reliability/item-response-theory/prox-model-example/): Describes how to build a PROX model for Rasch item response analysis in Excel using a specific example. The formulas in the spreadsheet are explained.
- [PROX Model for Rasch Analysis](https://real-statistics.com/reliability/item-response-theory/prox-model-rasch/): Describes how to build a PROX model (ability & difficulty are normally distributed) for Rasch item response theory analysis Examples and software are included.
- [Guessing](https://real-statistics.com/reliability/item-response-theory/guessing/): Describes how to use a Rasch model to detect when a subject is guessing and what to do about it. Examples are provided in Excel
- [Wright Map](https://real-statistics.com/reliability/item-response-theory/wright-map/): Describes how to create a Wright Map in Excel for use with Rasch item response analysis using Excel's charting capability.
- [Building a Rasch Model](https://real-statistics.com/reliability/item-response-theory/building-rasch-model/): Describes how to build a Rasch model in Excel and how to interpret the results. Also explains how good a fit the model is.
- [Rasch Analysis Basic Concepts](https://real-statistics.com/reliability/item-response-theory/rasch-analysis-basic-concepts/): Tutorial on Rasch item response analysis. Includes how to build a Rasch model for dichotomous data and how to interpret the model.
- [Rasch Analysis Motivation](https://real-statistics.com/reliability/item-response-theory/rasch-analysis-motivation/): Describes the motivation for performing Rasch analysis and the benefits obtained. This is the first of a series of tutorials on Rasch item response analysis.
- [Item Response Theory](https://real-statistics.com/reliability/item-response-theory/): Provides a tutorial on item response theory, with emphasis on testing using a Rasch model. Examples and software are provided.
- [Lin's Concordance Correlation Coefficient](https://real-statistics.com/reliability/interrater-reliability/lins-concordance-correlation-coefficient/): Describes Lin's concordance correlation coefficient and how to calculate it in Excel as well as a confidence interval. Also explains how to interpret Lin's CCC.
- [Real Statistics Support for Bland-Altman](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/real-statistics-support-bland-altman/): Describes, step-by-step, how to use the Real Statistics Bland-Altman data analysis tool to create a Bland-Altman Plot in Excel. An example is provided.
- [Confidence Interval for Bland-Altman](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/confidence-interval-bland-altman/): Describes how to calculate confidence intervals for Bland-Altman in Excel. Includes formula for the standard error, as well asexamples and software.
- [Limits of Agreement](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/limits-of-agreement/): Describes how to add the limits of agreement and mean (bias) to a Bland-Altman Plot in Excel. Also provides an example of advanced Excel charting techniques.
- [Bland-Altman Plot](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/bland-altman-plot/): Describes how to construct a Bland-Altman plot in Excel in order to compare two measurements of the same variable and decide to replace one with the other.
- [Bland-Altman Analysis](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/): Tutorial on Bland-Altman analysis. Describes how to construct a Bland-Altman Plot in Excel and provides examples and software to facilitate this
- [Kendall’s Coefficient of Concordance (W)](https://real-statistics.com/reliability/interrater-reliability/kendalls-w/): Tutorial on Kendall’s coefficient of concordance (W), including how to use and calculate it in Excel (even when there are ties).
- [Test Theory and Item Analysis](https://real-statistics.com/reliability/item-analysis/): Tutorial on item analysis in testing, including item discrimination, using the discrimination index, and item difficulty. Examples and software are provided.

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